Finite Group Databasebeta

← Group #72253937

Character table — Group #72253937

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222244444444444444444488888888888816161616161616161616161616161616161616161616161616161616161616161616161624242424242424242424242448484848484848484848
order122222344446662222224444446612121212666666121212121212224444444444666612121212121212121212121212121212121212124444888888882244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-1-1-1
χ91111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-11-11-1ii−i−i
χ101111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii-11-11-11−i−iii
χ111111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-11-11-1−i−iii
χ121111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i-11-11-11ii−i−i
χ131111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-111-1-11−i−iii
χ141111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii1-1-111-1ii−i−i
χ151111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-111-1-11ii−i−i
χ161111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i1-1-111-1−i−iii
χ17222222222222222-2-22-2-222-2-2-2-22222222-2-2-22-222-2-2-2-200000000000000000000000000000000000022220000000000-2-2000000
χ18222222222222222-2-22-2-222-2-2-2-22222222-2-2-22-222-2-2-2-2000000000000000000000000000000000000-2-2-2-2000000000022000000
χ1922222222222222-22-2-22-2-2-222-2-2222222-22-2-2-22-2-222-2-20000000000000000000000000000000000000000000000002200-2-20000
χ2022222222222222-22-2-22-2-2-222-2-2222222-22-2-2-22-2-222-2-2000000000000000000000000000000000000000000000000-2-200220000
χ2122222222222222-2-22-2-22-2-2-2-222222222-2-222-2-2-2-2-2-22222-2-2000000002222-2-2-2-200000000000000000000000000000000000000
χ2222222222222222-2-22-2-22-2-2-2-222222222-2-222-2-2-2-2-2-222-2-22200000000-2-2-2-2222200000000000000000000000000000000000000
χ232222222-2-2-2-222222-222-2-2-2-2-22222-2-2-2-222-2-222-2-2-2-2222-2-220000000022-2-2-2-22200000000000000000000000000000000000000
χ242222222-2-2-2-222222-222-2-2-2-2-22222-2-2-2-222-2-222-2-2-2-222-222-200000000-2-22222-2-200000000000000000000000000000000000000
χ252222222-2-2-2-22222-222-22-2-222-2-222-2-2-2-22-2222-2-2-222-2-20000000000000000000000000000000000000000000000002-200-220000
χ262222222-2-2-2-22222-222-22-2-222-2-222-2-2-2-22-2222-2-2-222-2-2000000000000000000000000000000000000000000000000-22002-20000
χ272222222-2-2-2-2222-222-22222-2-2-2-222-2-2-2-2-2222-2222-2-2-2-200000000000000000000000000000000000022-2-20000000000-22000000
χ282222222-2-2-2-2222-222-22222-2-2-2-222-2-2-2-2-2222-2222-2-2-2-2000000000000000000000000000000000000-2-22200000000002-2000000
χ29222222-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ30222222-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000000000
χ31222222-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000000000
χ32222222-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000000000
χ33222222-12222-1-1-1-2-22-2-22-2-2-2-222-1-1-1-1-1-111-1-1111111-1-122-2-200000000-1-1-1-1111133−3−333−3−333−3−333−3−30000000000000000000000
χ34222222-12222-1-1-1-2-22-2-22-2-2-2-222-1-1-1-1-1-111-1-1111111-1-122-2-200000000-1-1-1-11111−3−333−3−333−3−333−3−3330000000000000000000000
χ35222222-12222-1-1-1-2-22-2-22-2-2-2-222-1-1-1-1-1-111-1-1111111-1-1-2-222000000001111-1-1-1-133−3−333−3−3−3−333−3−3330000000000000000000000
χ36222222-12222-1-1-1-2-22-2-22-2-2-2-222-1-1-1-1-1-111-1-1111111-1-1-2-222000000001111-1-1-1-1−3−333−3−33333−3−333−3−30000000000000000000000
χ37222222-1-2-2-2-2-1-1-122-222-2-2-2-2-222-1-11111-1-111-1-11111-1-12-2-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000000000
χ38222222-1-2-2-2-2-1-1-122-222-2-2-2-2-222-1-11111-1-111-1-11111-1-12-2-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000000000
χ39222222-1-2-2-2-2-1-1-122-222-2-2-2-2-222-1-11111-1-111-1-11111-1-1-222-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000000000
χ40222222-1-2-2-2-2-1-1-122-222-2-2-2-2-222-1-11111-1-111-1-11111-1-1-222-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000000000
χ41222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2222222-1-11111111111-1-1-1-1-1-12-22-22i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000000000000000
χ42222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2222222-1-11111111111-1-1-1-1-1-12-22-2−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000000000000000
χ43222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2222222-1-11111111111-1-1-1-1-1-1-22-222i2i−2i−2i−2i−2i2i2i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000000000
χ44222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2222222-1-11111111111-1-1-1-1-1-1-22-22−2i−2i2i2i2i2i−2i−2i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000000000
χ4522-2-2-22222-2-2-2-2222-2-2-222-22-22-2-2222-2-2222-2-2-22-22-22-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ4622-2-2-22222-2-2-2-2222-2-2-222-22-22-2-2222-2-2222-2-2-22-22-22-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ4722-2-2-22222-2-2-2-222-22-22-22-2-22-22-2222-2-22-2-22-222-2-22-220000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ4822-2-2-22222-2-2-2-222-22-22-22-2-22-22-2222-2-22-2-22-222-2-22-22000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4922-2-2-22222-2-2-2-22-2222-2-2-222-2-22-2222-2-2-22-222-2-222-2-2200000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ5022-2-2-22222-2-2-2-22-2222-2-2-222-2-22-2222-2-2-22-222-2-222-2-220000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ5122-2-2-22222-2-2-2-22-2-2-2222-22-222-2-2222-2-2-2-22-222-22-222-200002-22-20000000000002-22-22-22-2000000000000000000000000000000
χ5222-2-2-22222-2-2-2-22-2-2-2222-22-222-2-2222-2-2-2-22-222-22-222-20000-22-22000000000000-22-22-22-22000000000000000000000000000000
χ5322-2-2-222-2-222-2-22222-2-2-2-22-222-2-22-2-22222-22-2-2-22-222-200002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ5422-2-2-222-2-222-2-22222-2-2-2-22-222-2-22-2-22222-22-2-2-22-222-20000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ5522-2-2-222-2-222-2-222-2-2-222-222-2-22-22-2-2222-22-2-22-222-2-22000000000000000000000000000000000000000022-2-2-2-2220000000000
χ5622-2-2-222-2-222-2-222-2-2-222-222-2-22-22-2-2222-22-2-22-222-2-220000000000000000000000000000000000000000-2-22222-2-20000000000
χ5722-2-2-222-2-222-2-22-22-22-222-2-22-22-22-2-222-222-22-22-2-22-220000000000000000000000000000000000000000000000000000002-2-22
χ5822-2-2-222-2-222-2-22-22-22-222-2-22-22-22-2-222-222-22-22-2-22-22000000000000000000000000000000000000000000000000000000-222-2
χ5922-2-2-222-2-222-2-22-2-2222-22-22-22-2-22-2-222-2-2-22222-22-22-2000000002-2-2200000000000000002-22-2-22-220000000000000000000000
χ6022-2-2-222-2-222-2-22-2-2222-22-22-22-2-22-2-222-2-2-22222-22-22-200000000-222-20000000000000000-22-222-22-20000000000000000000000
χ6122-2-2-22-122-2-211-122-2-2-222-22-22-21-1-1-111-1-1-1111-11-11-11000000002i−2i2i−2i−i3i3−i3i3−i3i3−i3i33−3−333−3−33−ii−ii−ii−ii0000000000000000000000
χ6222-2-2-22-122-2-211-122-2-2-222-22-22-21-1-1-111-1-1-1111-11-11-11000000002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−333−3−333−3−ii−ii−ii−ii0000000000000000000000
χ6322-2-2-22-122-2-211-122-2-2-222-22-22-21-1-1-111-1-1-1111-11-11-1100000000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3−333−3−333−3i−ii−ii−ii−i0000000000000000000000
χ6422-2-2-22-122-2-211-122-2-2-222-22-22-21-1-1-111-1-1-1111-11-11-1100000000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i33−3−333−3−33i−ii−ii−ii−i0000000000000000000000
χ6522-2-2-22-122-2-211-1-2-2-2222-22-222-21-1-1-11111-11-1-11-11-1-1100002-22-20000−i3i3−i3i3i3−i3i3−i3-11-11-11-11−i3i3i3−i3−i3i3i3−i30000000000000000000000
χ6622-2-2-22-122-2-211-1-2-2-2222-22-222-21-1-1-11111-11-1-11-11-1-1100002-22-20000i3−i3i3−i3−i3i3−i3i3-11-11-11-11i3−i3−i3i3i3−i3−i3i30000000000000000000000
χ6722-2-2-22-122-2-211-1-2-2-2222-22-222-21-1-1-11111-11-1-11-11-1-110000-22-220000−i3i3−i3i3i3−i3i3−i31-11-11-11-1i3−i3−i3i3i3−i3−i3i30000000000000000000000
χ6822-2-2-22-122-2-211-1-2-2-2222-22-222-21-1-1-11111-11-1-11-11-1-110000-22-220000i3−i3i3−i3−i3i3−i3i31-11-11-11-1−i3i3i3−i3−i3i3i3−i30000000000000000000000
χ6922-2-2-22-1-2-22211-1222-2-2-2-22-222-21-111-1-1-1-11-1111-11-1-1100002i−2i−2i2i0000−i3i3i3−i3i3−i3−i3i3−ii−iii−ii−i3−3−33−333−30000000000000000000000
χ7022-2-2-22-1-2-22211-1222-2-2-2-22-222-21-111-1-1-1-11-1111-11-1-1100002i−2i−2i2i0000i3−i3−i3i3−i3i3i3−i3−ii−iii−ii−i−333−33−3−330000000000000000000000
χ7122-2-2-22-1-2-22211-1222-2-2-2-22-222-21-111-1-1-1-11-1111-11-1-110000−2i2i2i−2i0000−i3i3i3−i3i3−i3−i3i3i−ii−i−ii−ii−333−33−3−330000000000000000000000
χ7222-2-2-22-1-2-22211-1222-2-2-2-22-222-21-111-1-1-1-11-1111-11-1-110000−2i2i2i−2i0000i3−i3−i3i3−i3i3i3−i3i−ii−i−ii−ii3−3−33−333−30000000000000000000000
χ7322-2-2-22-1-2-22211-1-2-2222-22-22-22-21-111-1-1111-1-1-1-11-11-11000000002-2-22−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3-11-111-11-10000000000000000000000
χ7422-2-2-22-1-2-22211-1-2-2222-22-22-22-21-111-1-1111-1-1-1-11-11-11000000002-2-22i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3-11-111-11-10000000000000000000000
χ7522-2-2-22-1-2-22211-1-2-2222-22-22-22-21-111-1-1111-1-1-1-11-11-1100000000-222-2−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i31-11-1-11-110000000000000000000000
χ7622-2-2-22-1-2-22211-1-2-2222-22-22-22-21-111-1-1111-1-1-1-11-11-1100000000-222-2i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i31-11-1-11-110000000000000000000000
χ77444444-24444-2-2-24-4-44-4-444-4-4-4-4-2-2-2-2-2-2-2222-22-2-222220000000000000000000000000000000000000000000000000000000000
χ78444444-24444-2-2-2-44-4-44-4-4-444-4-4-2-2-2-2-2-22-2222-222-2-2220000000000000000000000000000000000000000000000000000000000
χ79444444-2-4-4-4-4-2-2-24-444-44-4-444-4-4-2-22222-22-2-2-2222-2-2220000000000000000000000000000000000000000000000000000000000
χ80444444-2-4-4-4-4-2-2-2-444-44444-4-4-4-4-2-222222-2-2-22-2-2-222220000000000000000000000000000000000000000000000000000000000
χ814444-4-444-44-4444000000000000-4-44-44-400000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000
χ824444-4-444-44-4444000000000000-4-44-44-40000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000
χ834444-4-44-44-44444000000000000-4-4-44-4400000000000000000000000000000000000000000000000000002-22-2-22-220000000000
χ844444-4-44-44-44444000000000000-4-4-44-440000000000000000000000000000000000000000000000000000-22-222-22-20000000000
χ8544-4-44-444-4-44-4-440000000000004-44-4-4400000000000000000000000000000000000000000000000000002-2-222-2-220000000000
χ8644-4-44-444-4-44-4-440000000000004-44-4-440000000000000000000000000000000000000000000000000000-222-2-222-20000000000
χ8744-4-44-44-444-4-4-440000000000004-4-444-400000000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ8844-4-44-44-444-4-4-440000000000004-4-444-40000000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ8944-4-4-44-244-4-422-24-44-44-44-4-44-442-2-2-222-222-22-2-222-22-20000000000000000000000000000000000000000000000000000000000
χ9044-4-4-44-244-4-422-2-4444-4-4-444-4-442-2-2-2222-22-2-222-2-222-20000000000000000000000000000000000000000000000000000000000
χ9144-4-4-44-2-4-44422-24-4-4-444-444-4-442-222-2-2-22-222-22-2-222-20000000000000000000000000000000000000000000000000000000000
χ9244-4-4-44-2-4-44422-2-44-44-444-4-44-442-222-2-22-2-22-22-222-22-20000000000000000000000000000000000000000000000000000000000
χ938888-8-8-48-88-8-4-4-400000000000044-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ948888-8-8-4-88-88-4-4-4000000000000444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-88-8-48-8-8844-4000000000000-44-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-88-8-4-888-844-4000000000000-444-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ978-88-800800008-8-8000000000000000000000000000000000000000000000000000000000000000000004-4000000000000000000
χ988-88-800800008-8-800000000000000000000000000000000000000000000000000000000000000000000-44000000000000000000
χ998-8-880080000-88-80000000000000000000000000000000000000000000000000000000000000000004-400000000000000000000
χ1008-8-880080000-88-8000000000000000000000000000000000000000000000000000000000000000000-4400000000000000000000
χ10116-1616-1600-80000-8880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10216-16-161600-800008-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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