Finite Group Databasebeta

← Group #10713313

Character table — Group #10713313

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222222244444444444444444444444444444444888888888888888888888888242424242424242448484848
order1222223444444446668888121212121212121212121212446688888812121212121224242424242424242424242424242424888888882424242424242424242424242424242416161616161616164444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ101111-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ111111-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ121111-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111i−ii−i
χ131111-1-11-1-11111-1-11111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111i−i−ii
χ141111-1-11-1-11111-1-11111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−iii−i
χ151111-1-11-1-11111-1-11111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−iii−i
χ161111-1-11-1-11111-1-11111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1i−i−ii
χ17222222222222222222-2-2-2-22222222222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ18222222222-2-2-2-2-2-222200002222-2-2-2-2-2-2-2-2-2222000000-2-222-2-20000000000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ19222222222-2-2-2-2-2-222200002222-2-2-2-2-2-2-2-2-2222000000-2-222-2-20000000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ202222222-2-222-2-2-2-22220000-2-2-2-22222-2-2-2-22-22200000022-2-2-2-20000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ212222222-2-222-2-2-2-22220000-2-2-2-22222-2-2-2-22-22200000022-2-2-2-20000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22222-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ23222222-122222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ25222222-122222222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-1-1-1-1-1-1111111111111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ26222222-122222222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-1-1-1-1-1-1111111111111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ27222222-1-2-2-2-22222-1-1-1222211111111-1-1-1-1-2-2-1-122-2-2-2-21111-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ28222222-1-2-2-2-22222-1-1-1222211111111-1-1-1-1-2-2-1-122-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ29222222-1-2-2-2-22222-1-1-1-2-2-2-211111111-1-1-1-1-2-2-1-1-2-222221111-1-111111111-1-1-1-1-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ30222222-1-2-2-2-22222-1-1-1-2-2-2-211111111-1-1-1-1-2-2-1-1-2-222221111-1-111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ312222-2-222222-2-2222220000222222222222-2-2-2-2000000-2-2-2-2-2-20000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ322222-2-222222-2-2222220000222222222222-2-2-2-2000000-2-2-2-2-2-20000000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ332222-2-2222-2-222-2-2222-2-2-2-22222-2-2-2-2-2-2-2-22-2-2-222-2-22222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ342222-2-22-2-22222-2-2222-2-2-2-2-2-2-2-22222-2-2-2-2-22-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ352222-2-22-2-2-2-2-2-2222220000-2-2-2-2-2-2-2-2222222-2-20000002222-2-20000000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ362222-2-22-2-2-2-2-2-2222220000-2-2-2-2-2-2-2-2222222-2-20000002222-2-20000000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ372222-2-2-122-2-222-2-2-1-1-12222-1-1-1-1111111112-211-2-222-2-2-1-111-1-1-1-1-1-11111-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000
χ382222-2-2-122-2-222-2-2-1-1-12222-1-1-1-1111111112-211-2-222-2-2-1-111-1-1-1-1-1-11111-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000
χ392222-2-2-122-2-222-2-2-1-1-1-2-2-2-2-1-1-1-1111111112-21122-2-222-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−3−3−33333−3−3−3−333000000000000
χ402222-2-2-122-2-222-2-2-1-1-1-2-2-2-2-1-1-1-1111111112-21122-2-222-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−33333−3−3−3−33333−3−3000000000000
χ412222-2-2-1-2-22222-2-2-1-1-122221111-1-1-1-11111-2211-2-2-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ422222-2-2-1-2-22222-2-2-1-1-122221111-1-1-1-11111-2211-2-2-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000
χ432222-2-2-1-2-22222-2-2-1-1-1-2-2-2-21111-1-1-1-11111-22112222-2-211-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−3000000000000
χ442222-2-2-1-2-22222-2-2-1-1-1-2-2-2-21111-1-1-1-11111-22112222-2-211-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−333000000000000
χ4522-2-22-2200002-22-22-2-222-2-20000000022-2-2002-22-2000000002-222-2-222-2-20000000000002-22-2000000002-22-22-22-2000000000000
χ4622-2-22-2200002-22-22-2-222-2-20000000022-2-2002-22-2000000002-222-2-222-2-2000000000000-22-2200000000-22-22-22-22000000000000
χ4722-2-22-2200002-22-22-2-2-2-2220000000022-2-2002-2-22000000002-2-2-222-2-222000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ4822-2-22-2200002-22-22-2-2-2-2220000000022-2-2002-2-22000000002-2-2-222-2-22200000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ4922-2-22-2-100002-22-2-11122-2-233−3−333−3−3-1-11100-112-200003−33−3-11-1-111-1-11133−3−333−3−300002-22-23−3−333−3−33-11-11-11-11000000000000
χ5022-2-22-2-100002-22-2-11122-2-233−3−333−3−3-1-11100-112-200003−33−3-11-1-111-1-11133−3−333−3−30000-22-22−333−3−333−31-11-11-11-1000000000000
χ5122-2-22-2-100002-22-2-11122-2-2−3−333−3−333-1-11100-112-20000−33−33-11-1-111-1-111−3−333−3−33300002-22-2−333−3−333−3-11-11-11-11000000000000
χ5222-2-22-2-100002-22-2-11122-2-2−3−333−3−333-1-11100-112-20000−33−33-11-1-111-1-111−3−333−3−3330000-22-223−3−333−3−331-11-11-11-1000000000000
χ5322-2-22-2-100002-22-2-111-2-22233−3−333−3−3-1-11100-11-2200003−33−3-1111-1-111-1-1−3−333−3−3332i−2i2i−2i0000−ii−ii−ii−ii−i3i3i3−i3−i3i3i3−i3000000000000
χ5422-2-22-2-100002-22-2-111-2-22233−3−333−3−3-1-11100-11-2200003−33−3-1111-1-111-1-1−3−333−3−333−2i2i−2i2i0000i−ii−ii−ii−ii3−i3−i3i3i3−i3−i3i3000000000000
χ5522-2-22-2-100002-22-2-111-2-222−3−333−3−333-1-11100-11-220000−33−33-1111-1-111-1-133−3−333−3−32i−2i2i−2i0000−ii−ii−ii−iii3−i3−i3i3i3−i3−i3i3000000000000
χ5622-2-22-2-100002-22-2-111-2-222−3−333−3−333-1-11100-11-220000−33−33-1111-1-111-1-133−3−333−3−3−2i2i−2i2i0000i−ii−ii−ii−i−i3i3i3−i3−i3i3i3−i3000000000000
χ5722-2-2-22200002-2-222-2-222-2-200000000-2-22200-22-22000000002-222-2-2-2-2220000000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i000000000000
χ5822-2-2-22200002-2-222-2-222-2-200000000-2-22200-22-22000000002-222-2-2-2-222000000000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000000000
χ5922-2-2-22200002-2-222-2-2-2-22200000000-2-22200-222-2000000002-2-2-22222-2-2000000002-2-2200002-22-2-22-2200000000000000000000
χ6022-2-2-22200002-2-222-2-2-2-22200000000-2-22200-222-2000000002-2-2-22222-2-200000000-222-20000-22-222-22-200000000000000000000
χ6122-2-2-22-100002-2-22-11122-2-233−3−3−3−33311-1-1001-1-2200003−3−33-11-1-11111-1-133−3−3−3−33300002i−2i−2i2ii3−i3−i3i3−i3i3i3−i3−ii−iii−ii−i000000000000
χ6222-2-2-22-100002-2-22-11122-2-233−3−3−3−33311-1-1001-1-2200003−3−33-11-1-11111-1-133−3−3−3−3330000−2i2i2i−2i−i3i3i3−i3i3−i3−i3i3i−ii−i−ii−ii000000000000
χ6322-2-2-22-100002-2-22-11122-2-2−3−33333−3−311-1-1001-1-220000−333−3-11-1-11111-1-1−3−33333−3−300002i−2i−2i2i−i3i3i3−i3i3−i3−i3i3−ii−iii−ii−i000000000000
χ6422-2-2-22-100002-2-22-11122-2-2−3−33333−3−311-1-1001-1-220000−333−3-11-1-11111-1-1−3−33333−3−30000−2i2i2i−2ii3−i3−i3i3−i3i3i3−i3i−ii−i−ii−ii000000000000
χ6522-2-2-22-100002-2-22-111-2-22233−3−3−3−33311-1-1001-12-200003−3−33-1111-1-1-1-111−3−33333−3−32-2-220000-11-111-11-1−333−33−3−33000000000000
χ6622-2-2-22-100002-2-22-111-2-22233−3−3−3−33311-1-1001-12-200003−3−33-1111-1-1-1-111−3−33333−3−3-222-200001-11-1-11-113−3−33−333−3000000000000
χ6722-2-2-22-100002-2-22-111-2-222−3−33333−3−311-1-1001-12-20000−333−3-1111-1-1-1-11133−3−3−3−3332-2-220000-11-111-11-13−3−33−333−3000000000000
χ6822-2-2-22-100002-2-22-111-2-222−3−33333−3−311-1-1001-12-20000−333−3-1111-1-1-1-11133−3−3−3−333-222-200001-11-1-11-11−333−33−3−33000000000000
χ69444444-244-4-4-4-4-4-4-2-2-20000-2-2-2-222222222-44-2-200000022-2-2220000000000000000000000000000000000000000000000000000
χ70444444-2-4-444-4-4-4-4-2-2-200002222-2-2-2-222224-4-2-2000000-2-222220000000000000000000000000000000000000000000000000000
χ714444-4-4-24444-4-444-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-2-4-4220000002222220000000000000000000000000000000000000000000000000000
χ724444-4-4-2-4-4-4-4-4-444-2-2-2000022222222-2-2-2-24422000000-2-2-2-2220000000000000000000000000000000000000000000000000000
χ7344-4-44-440000-44-444-4-4000000000000-4-444004-40000000000-440000000000000000000000000000000000000000000000000000
χ7444-4-44-4-20000-44-44-22200002323−23−23−23−23232322-2-200-22000000−232323−232-20000000000000000000000000000000000000000000000000000
χ7544-4-44-4-20000-44-44-2220000−23−2323232323−23−2322-2-200-2200000023−23−23232-20000000000000000000000000000000000000000000000000000
χ7644-4-4-4440000-444-44-4-400000000000044-4-400-440000000000-440000000000000000000000000000000000000000000000000000
χ7744-4-4-44-20000-444-4-22200002323−23−232323−23−23-2-222002-2000000−2323−23232-20000000000000000000000000000000000000000000000000000
χ7844-4-4-44-20000-444-4-2220000−23−232323−23−232323-2-222002-200000023−2323−232-20000000000000000000000000000000000000000000000000000
χ794-44-4004004-40000-44-4−2i22i2−2i22i200004-44-4000000000000−2i22i2000000−2i22i2−2i22i200000000−2i22i2−2i22i2000000000000000000000000000000000000
χ804-44-4004004-40000-44-42i2−2i22i2−2i200004-44-40000000000002i2−2i20000002i2−2i22i2−2i2000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ814-44-400400-440000-44-4−2i22i2−2i22i20000-44-440000000000002i2−2i2000000−2i22i2−2i22i2000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ824-44-400400-440000-44-42i2−2i22i2−2i20000-44-44000000000000−2i22i20000002i2−2i22i2−2i200000000−2i22i2−2i22i2000000000000000000000000000000000000
χ834-44-400-2004-400002-22−2i22i2−2i22i223−2323−23-22-2223−2323−2300000000−2i22i2000000i2−i2i2−i2i6−i6i6−i6i6−i6i6−i6i2−i2i2−i2000000000000000000000000000000000000
χ844-44-400-2004-400002-22−2i22i2−2i22i2−2323−2323-22-22−2323−232300000000−2i22i2000000i2−i2i2−i2−i6i6−i6i6−i6i6−i6i6i2−i2i2−i2000000000000000000000000000000000000
χ854-44-400-2004-400002-222i2−2i22i2−2i223−2323−23-22-2223−2323−23000000002i2−2i2000000−i2i2−i2i2−i6i6−i6i6−i6i6−i6i6−i2i2−i2i2000000000000000000000000000000000000
χ864-44-400-2004-400002-222i2−2i22i2−2i2−2323−2323-22-22−2323−2323000000002i2−2i2000000−i2i2−i2i2i6−i6i6−i6i6−i6i6−i6−i2i2−i2i2000000000000000000000000000000000000
χ874-44-400-200-4400002-22−2i22i2−2i22i223−2323−232-22-2−2323−2323000000002i2−2i2000000i2−i2i2−i2−i6i6−i6i6i6−i6i6−i6−i2i2−i2i2000000000000000000000000000000000000
χ884-44-400-200-4400002-22−2i22i2−2i22i2−2323−23232-22-223−2323−23000000002i2−2i2000000i2−i2i2−i2i6−i6i6−i6−i6i6−i6i6−i2i2−i2i2000000000000000000000000000000000000
χ894-44-400-200-4400002-222i2−2i22i2−2i223−2323−232-22-2−2323−232300000000−2i22i2000000−i2i2−i2i2i6−i6i6−i6−i6i6−i6i6i2−i2i2−i2000000000000000000000000000000000000
χ904-44-400-200-4400002-222i2−2i22i2−2i2−2323−23232-22-223−2323−2300000000−2i22i2000000−i2i2−i2i2−i6i6−i6i6i6−i6i6−i6i2−i2i2−i2000000000000000000000000000000000000
χ914-4-440044-4000000-4-44−2i22i22i2−2i24-4-4400000000000000−2i22i200000000−2i22i22i2−2i200002i2−2i2−2i22i20000000000000000000000000000000000000000
χ924-4-440044-4000000-4-442i2−2i2−2i22i24-4-44000000000000002i2−2i2000000002i2−2i2−2i22i20000−2i22i22i2−2i20000000000000000000000000000000000000000
χ934-4-44004-44000000-4-44−2i22i22i2−2i2-444-4000000000000002i2−2i200000000−2i22i22i2−2i20000−2i22i22i2−2i20000000000000000000000000000000000000000
χ944-4-44004-44000000-4-442i2−2i2−2i22i2-444-400000000000000−2i22i2000000002i2−2i2−2i22i200002i2−2i2−2i22i20000000000000000000000000000000000000000
χ954-4-4400-24-400000022-2−2i22i22i2−2i2-222-223−23−2323−232323−23000000−2i22i200000000i2−i2−i2i2−i6i6i6−i6−i2i2i2−i2−i6i6i6−i6000000000000000000000000000000000000
χ964-4-4400-24-400000022-2−2i22i22i2−2i2-222-2−232323−2323−23−2323000000−2i22i200000000i2−i2−i2i2i6−i6−i6i6−i2i2i2−i2i6−i6−i6i6000000000000000000000000000000000000
χ974-4-4400-24-400000022-22i2−2i2−2i22i2-222-223−23−2323−232323−230000002i2−2i200000000−i2i2i2−i2i6−i6−i6i6i2−i2−i2i2i6−i6−i6i6000000000000000000000000000000000000
χ984-4-4400-24-400000022-22i2−2i2−2i22i2-222-2−232323−2323−23−23230000002i2−2i200000000−i2i2i2−i2−i6i6i6−i6i2−i2−i2i2−i6i6i6−i6000000000000000000000000000000000000
χ994-4-4400-2-4400000022-2−2i22i22i2−2i22-2-2223−23−232323−23−23230000002i2−2i200000000i2−i2−i2i2i6−i6−i6i6i2−i2−i2i2−i6i6i6−i6000000000000000000000000000000000000
χ1004-4-4400-2-4400000022-2−2i22i22i2−2i22-2-22−232323−23−232323−230000002i2−2i200000000i2−i2−i2i2−i6i6i6−i6i2−i2−i2i2i6−i6−i6i6000000000000000000000000000000000000
χ1014-4-4400-2-4400000022-22i2−2i2−2i22i22-2-2223−23−232323−23−2323000000−2i22i200000000−i2i2i2−i2−i6i6i6−i6−i2i2i2−i2i6−i6−i6i6000000000000000000000000000000000000
χ1024-4-4400-2-4400000022-22i2−2i2−2i22i22-2-22−232323−23−232323−23000000−2i22i200000000−i2i2i2−i2i6−i6−i6i6−i2i2i2−i2−i6i6i6−i6000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).