Finite Group Databasebeta

← Group #10713680

Character table — Group #10713680

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222222244444444444444444444444444444444888888888888888888888888242424242424242448484848
order1222223444444446668888121212121212121212121212446688888812121212121224242424242424242424242424242424888888882424242424242424242424242424242416161616161616162244
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
χ91111-1-1111-1-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-1111-1-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-1111-1-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-1111-1-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-11-1-11111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-11-1-11111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-11-1-11111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-11-1-11111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
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
χ312222-2-222222-2-2222220000222222222222-2-2-2-2000000-2-2-2-2-2-200000000000000000000000000000000000000002−2−222−2−220000
χ322222-2-222222-2-2222220000222222222222-2-2-2-2000000-2-2-2-2-2-20000000000000000000000000000000000000000−222−2−222−20000
χ332222-2-2222-2-222-2-222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-22222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ342222-2-22-2-22222-2-22222222-2-2-2-22222-2-2-2-2-22-2-2-2-222-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ352222-2-22-2-2-2-2-2-2222220000-2-2-2-2-2-2-2-2222222-2-20000002222-2-200000000000000000000000000000000000000002−2−22−222−20000
χ362222-2-22-2-2-2-2-2-2222220000-2-2-2-2-2-2-2-2222222-2-20000002222-2-20000000000000000000000000000000000000000−222−22−2−220000
χ372222-2-2-122-2-222-2-2-1-1-12222-1-1-1-1111111112-211-2-2-2-222-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−3−3−33333−3−3−3−333000000000000
χ382222-2-2-122-2-222-2-2-1-1-12222-1-1-1-1111111112-211-2-2-2-222-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−33333−3−3−3−33333−3−3000000000000
χ392222-2-2-122-2-222-2-2-1-1-1-2-2-2-2-1-1-1-1111111112-2112222-2-2-1-111-1-1-1-1-1-11111-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000
χ402222-2-2-122-2-222-2-2-1-1-1-2-2-2-2-1-1-1-1111111112-2112222-2-2-1-111-1-1-1-1-1-11111-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000
χ412222-2-2-1-2-22222-2-2-1-1-122221111-1-1-1-11111-2211-2-222-2-211-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−3000000000000
χ422222-2-2-1-2-22222-2-2-1-1-122221111-1-1-1-11111-2211-2-222-2-211-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−333000000000000
χ432222-2-2-1-2-22222-2-2-1-1-1-2-2-2-21111-1-1-1-11111-221122-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ442222-2-2-1-2-22222-2-2-1-1-1-2-2-2-21111-1-1-1-11111-221122-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000
χ452-2-222-2200002-22-22-2-222-2-20000000022-2-2002-22-2000000002-222-2-222-2-20000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000
χ462-2-222-2200002-22-22-2-222-2-20000000022-2-2002-22-2000000002-222-2-222-2-2000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000
χ472-2-222-2200002-22-22-2-2-2-2220000000022-2-2002-2-22000000002-2-2-222-2-222000000002-22-200002-22-22-22-200000000000000000000
χ482-2-222-2200002-22-22-2-2-2-2220000000022-2-2002-2-22000000002-2-2-222-2-22200000000-22-220000-22-22-22-2200000000000000000000
χ492-2-222-2-100002-22-2-11122-2-233−3−333−3−3-1-11100-112-200003−33−3-11-1-111-1-11133−3−333−3−300002i−2i2i−2i−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii000000000000
χ502-2-222-2-100002-22-2-11122-2-233−3−333−3−3-1-11100-112-200003−33−3-11-1-111-1-11133−3−333−3−30000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i000000000000
χ512-2-222-2-100002-22-2-11122-2-2−3−333−3−333-1-11100-112-20000−33−33-11-1-111-1-111−3−333−3−33300002i−2i2i−2ii3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii000000000000
χ522-2-222-2-100002-22-2-11122-2-2−3−333−3−333-1-11100-112-20000−33−33-11-1-111-1-111−3−333−3−3330000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i000000000000
χ532-2-222-2-100002-22-2-111-2-22233−3−333−3−3-1-11100-11-2200003−33−3-1111-1-111-1-1−3−333−3−3332-22-20000-11-11-11-113−3−333−3−33000000000000
χ542-2-222-2-100002-22-2-111-2-22233−3−333−3−3-1-11100-11-2200003−33−3-1111-1-111-1-1−3−333−3−333-22-2200001-11-11-11-1−333−3−333−3000000000000
χ552-2-222-2-100002-22-2-111-2-222−3−333−3−333-1-11100-11-220000−33−33-1111-1-111-1-133−3−333−3−32-22-20000-11-11-11-11−333−3−333−3000000000000
χ562-2-222-2-100002-22-2-111-2-222−3−333−3−333-1-11100-11-220000−33−33-1111-1-111-1-133−3−333−3−3-22-2200001-11-11-11-13−3−333−3−33000000000000
χ572-2-22-22200002-2-222-2-222-2-200000000-2-22200-22-22000000002-2-2-22222-2-2000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ582-2-22-22200002-2-222-2-222-2-200000000-2-22200-22-22000000002-2-2-22222-2-200000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ592-2-22-22200002-2-222-2-2-2-22200000000-2-22200-222-2000000002-222-2-2-2-2220000000000002-2-22000000002-22-2-22-22000000000000
χ602-2-22-22200002-2-222-2-2-2-22200000000-2-22200-222-2000000002-222-2-2-2-222000000000000-222-200000000-22-222-22-2000000000000
χ612-2-22-22-100002-2-22-11122-2-233−3−3−3−33311-1-1001-1-2200003−3−33-1111-1-1-1-111−3−33333−3−32i−2i−2i2i0000−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i3000000000000
χ622-2-22-22-100002-2-22-11122-2-233−3−3−3−33311-1-1001-1-2200003−3−33-1111-1-1-1-111−3−33333−3−3−2i2i2i−2i0000i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i3000000000000
χ632-2-22-22-100002-2-22-11122-2-2−3−33333−3−311-1-1001-1-220000−333−3-1111-1-1-1-11133−3−3−3−3332i−2i−2i2i0000−ii−iii−ii−i−i3i3i3−i3i3−i3−i3i3000000000000
χ642-2-22-22-100002-2-22-11122-2-2−3−33333−3−311-1-1001-1-220000−333−3-1111-1-1-1-11133−3−3−3−333−2i2i2i−2i0000i−ii−i−ii−iii3−i3−i3i3−i3i3i3−i3000000000000
χ652-2-22-22-100002-2-22-111-2-22233−3−3−3−33311-1-1001-12-200003−3−33-11-1-11111-1-133−3−3−3−33300002-2-22−333−33−3−33-11-111-11-1000000000000
χ662-2-22-22-100002-2-22-111-2-22233−3−3−3−33311-1-1001-12-200003−3−33-11-1-11111-1-133−3−3−3−3330000-222-23−3−33−333−31-11-1-11-11000000000000
χ672-2-22-22-100002-2-22-111-2-222−3−33333−3−311-1-1001-12-20000−333−3-11-1-11111-1-1−3−33333−3−300002-2-223−3−33−333−3-11-111-11-1000000000000
χ682-2-22-22-100002-2-22-111-2-222−3−33333−3−311-1-1001-12-20000−333−3-11-1-11111-1-1−3−33333−3−30000-222-2−333−33−3−331-11-1-11-11000000000000
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
χ7344-4-4004004i−4i0000-44-422−2222−2200004i−4i4i−4i0000000000−2i22i200000000000022−2222−22−2i22i2−2i22i20000000000000000000000000000000000000000
χ7444-4-4004004i−4i0000-44-4−2222−222200004i−4i4i−4i00000000002i2−2i2000000000000−2222−22222i2−2i22i2−2i20000000000000000000000000000000000000000
χ7544-4-400400−4i4i0000-44-422−2222−220000−4i4i−4i4i00000000002i2−2i200000000000022−2222−222i2−2i22i2−2i20000000000000000000000000000000000000000
χ7644-4-400400−4i4i0000-44-4−2222−22220000−4i4i−4i4i0000000000−2i22i2000000000000−2222−2222−2i22i2−2i22i20000000000000000000000000000000000000000
χ7744-4-400-2004i−4i00002-2222−2222−22−2i32i3−2i32i3−2i2i−2i2i23−2323−23000000−2i22i2000000006−66−6−22−22i2−i2i2−i2i6−i6i6−i6000000000000000000000000000000000000
χ7844-4-400-2004i−4i00002-2222−2222−222i3−2i32i3−2i3−2i2i−2i2i−2323−2323000000−2i22i200000000−66−66−22−22i2−i2i2−i2−i6i6−i6i6000000000000000000000000000000000000
χ7944-4-400-2004i−4i00002-22−2222−2222−2i32i3−2i32i3−2i2i−2i2i23−2323−230000002i2−2i200000000−66−662−22−2−i2i2−i2i2−i6i6−i6i6000000000000000000000000000000000000
χ8044-4-400-2004i−4i00002-22−2222−22222i3−2i32i3−2i3−2i2i−2i2i−2323−23230000002i2−2i2000000006−66−62−22−2−i2i2−i2i2i6−i6i6−i6000000000000000000000000000000000000
χ8144-4-400-200−4i4i00002-2222−2222−22−2i32i3−2i32i32i−2i2i−2i−2323−23230000002i2−2i200000000−66−66−22−22−i2i2−i2i2i6−i6i6−i6000000000000000000000000000000000000
χ8244-4-400-200−4i4i00002-2222−2222−222i3−2i32i3−2i32i−2i2i−2i23−2323−230000002i2−2i2000000006−66−6−22−22−i2i2−i2i2−i6i6−i6i6000000000000000000000000000000000000
χ8344-4-400-200−4i4i00002-22−2222−2222−2i32i3−2i32i32i−2i2i−2i−2323−2323000000−2i22i2000000006−66−62−22−2i2−i2i2−i2−i6i6−i6i6000000000000000000000000000000000000
χ8444-4-400-200−4i4i00002-22−2222−22222i3−2i32i3−2i32i−2i2i−2i23−2323−23000000−2i22i200000000−66−662−22−2i2−i2i2−i2i6−i6i6−i6000000000000000000000000000000000000
χ854-44-40044i−4i000000-4-4422−22−22224i−4i−4i4i0000000000000000−2i22i2000000000022−22−22220000−2i22i22i2−2i2000000000000000000000000000000000000
χ864-44-40044i−4i000000-4-44−222222−224i−4i−4i4i00000000000000002i2−2i20000000000−222222−2200002i2−2i2−2i22i2000000000000000000000000000000000000
χ874-44-4004−4i4i000000-4-4422−22−2222−4i4i4i−4i00000000000000002i2−2i2000000000022−22−222200002i2−2i2−2i22i2000000000000000000000000000000000000
χ884-44-4004−4i4i000000-4-44−222222−22−4i4i4i−4i0000000000000000−2i22i20000000000−222222−220000−2i22i22i2−2i2000000000000000000000000000000000000
χ894-44-400-24i−4i00000022-222−22−2222−2i2i2i−2i−2i32i32i3−2i3−232323−2300000000−2i22i2000000−666−6−222−2i6−i6−i6i6i2−i2−i2i2000000000000000000000000000000000000
χ904-44-400-24i−4i00000022-222−22−2222−2i2i2i−2i2i3−2i3−2i32i323−23−232300000000−2i22i20000006−6−66−222−2−i6i6i6−i6i2−i2−i2i2000000000000000000000000000000000000
χ914-44-400-24i−4i00000022-2−222222−22−2i2i2i−2i−2i32i32i3−2i3−232323−23000000002i2−2i20000006−6−662−2−22−i6i6i6−i6−i2i2i2−i2000000000000000000000000000000000000
χ924-44-400-24i−4i00000022-2−222222−22−2i2i2i−2i2i3−2i3−2i32i323−23−2323000000002i2−2i2000000−666−62−2−22i6−i6−i6i6−i2i2i2−i2000000000000000000000000000000000000
χ934-44-400-2−4i4i00000022-222−22−22222i−2i−2i2i−2i32i32i3−2i323−23−2323000000002i2−2i20000006−6−66−222−2i6−i6−i6i6−i2i2i2−i2000000000000000000000000000000000000
χ944-44-400-2−4i4i00000022-222−22−22222i−2i−2i2i2i3−2i3−2i32i3−232323−23000000002i2−2i2000000−666−6−222−2−i6i6i6−i6−i2i2i2−i2000000000000000000000000000000000000
χ954-44-400-2−4i4i00000022-2−222222−222i−2i−2i2i−2i32i32i3−2i323−23−232300000000−2i22i2000000−666−62−2−22−i6i6i6−i6i2−i2−i2i2000000000000000000000000000000000000
χ964-44-400-2−4i4i00000022-2−222222−222i−2i−2i2i2i3−2i3−2i32i3−232323−2300000000−2i22i20000006−6−662−2−22i6−i6−i6i6i2−i2−i2i2000000000000000000000000000000000000
χ974-4-444-440000-44-444-4-4000000000000-4-444004-40000000000-440000000000000000000000000000000000000000000000000000
χ984-4-444-4-20000-44-44-22200002323−23−23−23−23232322-2-200-22000000−232323−232-20000000000000000000000000000000000000000000000000000
χ994-4-444-4-20000-44-44-2220000−23−2323232323−23−2322-2-200-2200000023−23−23232-20000000000000000000000000000000000000000000000000000
χ1004-4-44-4440000-444-44-4-400000000000044-4-400-440000000000-440000000000000000000000000000000000000000000000000000
χ1014-4-44-44-20000-444-4-22200002323−23−232323−23−23-2-222002-2000000−2323−23232-20000000000000000000000000000000000000000000000000000
χ1024-4-44-44-20000-444-4-2220000−23−232323−23−232323-2-222002-200000023−2323−232-20000000000000000000000000000000000000000000000000000

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