Finite Group Databasebeta

← Group #11786658

Character table — Group #11786658

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222444444444444444444448888888888888888888888121212121212121224242424242424242424242424242424242424243636363636363636
order1244222334446612121212366666666612121212121212121212668812122424242424242424242424242424242422448888668888121224242424242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1
χ911-1-11-1-11111-111-1-1-1-111-1-11-1-1-1-111-1-1-1-1111111-11-11-111111111-1-1-1-1-1-1-1-111-1-1ii−i−i11i−i1-1-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ1011-1-11-1-11111-111-1-1-1-111-1-11-1-1-1-111-1-1-1-1111111-11-11-111111111-1-1-1-1-1-1-1-111-1-1−i−iii11−ii1-1-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ1111-1-11-1-11111-111-1-1-1-111-1-11-1-1-1-111-1-1-1-1111111-11-11-111111111-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1i−i-1111ii−i−iii−i−i-1-111−i−iii−i−iii
χ1211-1-11-1-11111-111-1-1-1-111-1-11-1-1-1-111-1-1-1-1111111-11-11-111111111-1-1-1-1-1-1-1-1-1-111−i−iii-1-1−ii-1111−i−iii−i−iii-1-111ii−i−iii−i−i
χ1311-1-11-1-11111-111-1-1-1-111-1-11-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11111111111-1-1ii−i−i11−ii-11-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ1411-1-11-1-11111-111-1-1-1-111-1-11-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11111111111-1-1−i−iii11i−i-11-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ1511-1-11-1-11111-111-1-1-1-111-1-11-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-111111111-1-111ii−i−i-1-1−ii1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ1611-1-11-1-11111-111-1-1-1-111-1-11-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-111111111-1-111−i−iii-1-1i−i1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222222-12222-1-1-122-1222-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-122220000-1-10022-1-100000000-1-1-1-100000000
χ1822222222-12222-1-1-122-1222-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200001100-2-21100000000111100000000
χ1922222222-12222-1-1-122-1222-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-2-2-1-1-2-2111111-2-211111122220000-1-100-2-2-1-100000000111100000000
χ2022222222-12222-1-1-122-1222-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-2-2-1-1-2-2111111-2-2111111-2-2-2-200001100221100000000-1-1-1-100000000
χ212222222-12222-1222-1-1-1-1-1-1222-1-1-1-1-12-1-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-10000222200220000-1-1-1-1-1-1-1-1000000000000
χ222222222-12222-1222-1-1-1-1-1-1222-1-1-1-1-12-1-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-200-2-2000011111111000000000000
χ232222222-12222-1222-1-1-1-1-1-1222-1-1-1-1-12-1-1-12-1-12-1-1-2-2-1-111-2-2111111-2-211110000222200-2-20000-1-1-1-11111000000000000
χ242222222-12222-1222-1-1-1-1-1-1222-1-1-1-1-12-1-1-12-1-12-1-1-2-2-1-111-2-2111111-2-211110000-2-2-2-2002200001111-1-1-1-1000000000000
χ2522222-2-222-2-2222222222-2-22-2-2-2-22-22222-2-2-2-2-22-200-2200000000000000002-22-200002-200002-200000000000000000000
χ2622222-2-222-2-2222222222-2-22-2-2-2-22-22222-2-2-2-2-22-200-220000000000000000-22-220000-220000-2200000000000000000000
χ2722222-2-22-1-2-222-1-1-122-12-2-2-11111-1-22-1-1-1-21111-11001-1003−333−3−3003−333−3−32-22-20000-110000-11000000003−33−300000000
χ2822222-2-22-1-2-222-1-1-122-12-2-2-11111-1-22-1-1-1-21111-11001-1003−333−3−3003−333−3−3-22-2200001-100001-100000000−33−3300000000
χ2922222-2-22-1-2-222-1-1-122-12-2-2-11111-1-22-1-1-1-21111-11001-100−33−3−33300−33−3−3332-22-20000-110000-1100000000−33−3300000000
χ3022222-2-22-1-2-222-1-1-122-12-2-2-11111-1-22-1-1-1-21111-11001-100−33−3−33300−33−3−333-22-2200001-100001-1000000003−33−300000000
χ312222-22-2222-2-22222222-22-2-22-2222-2-2-2222222-2-2-200-2-2000000000000000000002-22-2000000002-22-20000000000000000
χ322222-22-2222-2-22222222-22-2-22-2222-2-2-2222222-2-2-200-2-200000000000000000000-22-2200000000-22-220000000000000000
χ332222-22-2-122-2-2-1222-1-1-11-11-22-2-1-1-111-2-1-1-12-1-1-2110011−i3i300−i3i3−i3i3−i3i300−i3i3−i3i300002-22-200000000-11-11−i3i3−i3i3000000000000
χ342222-22-2-122-2-2-1222-1-1-11-11-22-2-1-1-111-2-1-1-12-1-1-2110011−i3i300−i3i3−i3i3−i3i300−i3i3−i3i30000-22-22000000001-11-1i3−i3i3−i3000000000000
χ352222-22-2-122-2-2-1222-1-1-11-11-22-2-1-1-111-2-1-1-12-1-1-2110011i3−i300i3−i3i3−i3i3−i300i3−i3i3−i300002-22-200000000-11-11i3−i3i3−i3000000000000
χ362222-22-2-122-2-2-1222-1-1-11-11-22-2-1-1-111-2-1-1-12-1-1-2110011i3−i300i3−i3i3−i3i3−i300i3−i3i3−i30000-22-22000000001-11-1−i3i3−i3i3000000000000
χ372222-2-2222-22-22222222-2-22-2-22-2-222-2-222-2-2-2-22-22002-2000000000000000000000000000000000000000000002-22-20000
χ382222-2-2222-22-22222222-2-22-2-22-2-222-2-222-2-2-2-22-22002-200000000000000000000000000000000000000000000-22-220000
χ3922-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22200-2-200000000000000002-2-2200002-20000-2200000000000000000000
χ4022-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22200-2-20000000000000000-222-20000-2200002-200000000000000000000
χ4122-2-22222-1-2-2-22-111-2-2-1222-1-1-1-1-1-1-2-2111-21111-1-10011003−333−3−300−33−3−3332-2-220000-1100001-1000000003−3−3300000000
χ4222-2-22222-1-2-2-22-111-2-2-1222-1-1-1-1-1-1-2-2111-21111-1-10011003−333−3−300−33−3−333-222-200001-10000-1100000000−333−300000000
χ4322-2-22222-1-2-2-22-111-2-2-1222-1-1-1-1-1-1-2-2111-21111-1-1001100−33−3−333003−333−3−32-2-220000-1100001-100000000−333−300000000
χ4422-2-22222-1-2-2-22-111-2-2-1222-1-1-1-1-1-1-2-2111-21111-1-1001100−33−3−333003−333−3−3-222-200001-10000-11000000003−3−3300000000
χ4522-2-22-2-22-122-22-111-2-2-12-2-2-11111-12-21112-1-1-1-1-112-2-1122-1-1-1-1-1-1-2-211111122-2-20000-1-1002-21100000000-1-11100000000
χ4622-2-22-2-22-122-22-111-2-2-12-2-2-11111-12-21112-1-1-1-1-112-2-1122-1-1-1-1-1-1-2-2111111-2-22200001100-22-1-10000000011-1-100000000
χ4722-2-22-2-22-122-22-111-2-2-12-2-2-11111-12-21112-1-1-1-1-11-22-11-2-211111122-1-1-1-1-1-122-2-20000-1-100-22110000000011-1-100000000
χ4822-2-22-2-22-122-22-111-2-2-12-2-2-11111-12-21112-1-1-1-1-11-22-11-2-211111122-1-1-1-1-1-1-2-222000011002-2-1-100000000-1-11100000000
χ4922-2-22-2-2-1222-2-12-2-211-1-1112-2-211-1-11-211-12-1-12-112-2-11-1-122-1-1-1-111-2-2111100002i2i−2i−2i002i−2i0000−i−iii−i−iii000000000000
χ5022-2-22-2-2-1222-2-12-2-211-1-1112-2-211-1-11-211-12-1-12-112-2-11-1-122-1-1-1-111-2-211110000−2i−2i2i2i00−2i2i0000ii−i−iii−i−i000000000000
χ5122-2-22-2-2-1222-2-12-2-211-1-1112-2-211-1-11-211-12-1-12-11-22-1111-2-21111-1-122-1-1-1-100002i2i−2i−2i00−2i2i0000−i−iiiii−i−i000000000000
χ5222-2-22-2-2-1222-2-12-2-211-1-1112-2-211-1-11-211-12-1-12-11-22-1111-2-21111-1-122-1-1-1-10000−2i−2i2i2i002i−2i0000ii−i−i−i−iii000000000000
χ5322-2-2-22-222-22222-2-2-2-22-22-2-22-2222222-2-2-2-2-2-22-2-20022000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5422-2-2-22-222-22222-2-2-2-22-22-2-22-2222222-2-2-2-2-2-22-2-2002200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ5522-2-2-2-22222-2222-2-2-2-22-2-22-2-22-2-22-222-2-22222-2-2200-22000000000000000000002i−2i−2i2i000000002i−2i−2i2i0000000000000000
χ5622-2-2-2-22222-2222-2-2-2-22-2-22-2-22-2-22-222-2-22222-2-2200-2200000000000000000000−2i2i2i−2i00000000−2i2i2i−2i0000000000000000
χ5722-2-2-2-22-122-22-12-2-211-111-1-2-2211-11-1211-12-1-1-21-1001-1−i3i300−i3i3−i3i3i3−i300i3−i3i3−i300002i−2i−2i2i00000000−iii−i3−3−33000000000000
χ5822-2-2-2-22-122-22-12-2-211-111-1-2-2211-11-1211-12-1-1-21-1001-1−i3i300−i3i3−i3i3i3−i300i3−i3i3−i30000−2i2i2i−2i00000000i−i−ii−333−3000000000000
χ5922-2-2-2-22-122-22-12-2-211-111-1-2-2211-11-1211-12-1-1-21-1001-1i3−i300i3−i3i3−i3−i3i300−i3i3−i3i300002i−2i−2i2i00000000−iii−i−333−3000000000000
χ6022-2-2-2-22-122-22-12-2-211-111-1-2-2211-11-1211-12-1-1-21-1001-1i3−i300i3−i3i3−i3−i3i300−i3i3−i3i30000−2i2i2i−2i00000000i−i−ii3−3−33000000000000
χ614444444-2-2444-2-2-2-2-2-21-2-2-2-2-2-2111-2-2-211-2-211-2114411-2-2-2-21111-2-2-2-21111000000000000000000000000000000000000
χ624444444-2-2444-2-2-2-2-2-21-2-2-2-2-2-2111-2-2-211-2-211-211-4-4112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ6344444-4-4-24-4-44-2444-2-2-2-2224-4-422-22-24-2-22-422-4-22002-20000000000000000000000000000000000000000000000000000
χ6444444-4-4-2-2-4-44-2-2-2-2-2-21-222-222-1-112-2-21122-1-121-100-110023−23−3−3330023−23−3−333000000000000000000000000000000000000
χ6544444-4-4-2-2-4-44-2-2-2-2-2-21-222-222-1-112-2-21122-1-121-100-1100−232333−3−300−232333−3−3000000000000000000000000000000000000
χ664444-44-44-24-4-44-2-2-244-2-44-42-22-2-2-2-4-42-2-24-2-2-222200220000000000000000000000000000000000000000000000000000
χ674444-44-4-2-24-4-4-2-2-2-2-2-212-222-2211122211-2-2112-1-100-1-1−2i32i300i3−i3i3−i3−2i32i300i3−i3i3−i3000000000000000000000000000000000000
χ684444-44-4-2-24-4-4-2-2-2-2-2-212-222-2211122211-2-2112-1-100-1-12i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i3000000000000000000000000000000000000
χ694444-4-444-2-44-44-2-2-244-2-4-4422-222-24-42-2-2-4222-22-200-220000000000000000000000000000000000000000000000000000
χ704444-4-44-24-44-4-2444-2-2-222-2-4-4422-2-22-4-2-22-42242-200-220000000000000000000000000000000000000000000000000000
χ714444-4-44-2-2-44-4-2-2-2-2-2-2122-222-2-1-11-2221122-1-1-2-11001-100003i−3i−3i3i00003i−3i−3i3i000000000000000000000000000000000000
χ724444-4-44-2-2-44-4-2-2-2-2-2-2122-222-2-1-11-2221122-1-1-2-11001-10000−3i3i3i−3i0000−3i3i3i−3i000000000000000000000000000000000000
χ7344-4-4444-24-4-4-4-24-4-422-2-2-2-2444-2-2-222-4222-422-4-2-200220000000000000000000000000000000000000000000000000000
χ7444-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2-2111222-1-122-1-121100-1-10023−23−3−33300−232333−3−3000000000000000000000000000000000000
χ7544-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2-2111222-1-122-1-121100-1-100−232333−3−30023−23−3−333000000000000000000000000000000000000
χ7644-4-44-4-4-2-244-4-2-222221-222-222-1-11-222-1-1-2-211-21-14-41-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000000
χ7744-4-44-4-4-2-244-4-2-222221-222-222-1-11-222-1-1-2-211-21-1-441-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000000
χ7844-4-4-44-44-2-4444-222-4-4-2-44-42-22-2-2-244-222-4222-22200-2-20000000000000000000000000000000000000000000000000000
χ7944-4-4-44-4-24-444-24-4-422-22-22-44-4-2-2-2-2-24222-42242200-2-20000000000000000000000000000000000000000000000000000
χ8044-4-4-44-4-2-2-444-2-2222212-222-22111-2-2-2-1-122-1-1-2-1-1001100003i−3i−3i3i0000−3i3i3i−3i000000000000000000000000000000000000
χ8144-4-4-44-4-2-2-444-2-2222212-222-22111-2-2-2-1-122-1-1-2-1-100110000−3i3i3i−3i00003i−3i−3i3i000000000000000000000000000000000000
χ8244-4-4-4-444-24-444-222-4-4-2-4-4422-222-2-44-2224-2-2-222-2002-20000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-2-24-44-2-22222122-222-2-1-112-2-2-1-1-2-2112-1100-11−2i32i300i3−i3i3−i32i3−2i300−i3i3−i3i3000000000000000000000000000000000000
χ8444-4-4-4-44-2-24-44-2-22222122-222-2-1-112-2-2-1-1-2-2112-1100-112i3−2i300−i3i3−i3i3−2i32i300i3−i3i3−i3000000000000000000000000000000000000
χ854-44i−4i00044000-4-44i−4i4i−4i400000000-40004i−4i000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ864-44i−4i00044000-4-44i−4i4i−4i400000000-40004i−4i00000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ874-4−4i4i00044000-4-4−4i4i−4i4i400000000-4000−4i4i00000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ884-4−4i4i00044000-4-4−4i4i−4i4i400000000-4000−4i4i000000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ898-88i−8i0008-4000-84−4i4i8i−8i-4000000004000−4i4i000000000000000000000000000000000000000000000000000000000000000
χ908-88i−8i000-480004-88i−8i−4i4i-4000000004000−4i4i000000000000000000000000000000000000000000000000000000000000000
χ918-88i−8i000-4-400044−4i4i−4i4i20000006-6-20002i−2i006i−6i00000000000000000000000000000000000000000000000000000000000
χ928-88i−8i000-4-400044−4i4i−4i4i2000000-66-20002i−2i00−6i6i00000000000000000000000000000000000000000000000000000000000
χ938-8−8i8i0008-4000-844i−4i−8i8i-40000000040004i−4i000000000000000000000000000000000000000000000000000000000000000
χ948-8−8i8i000-480004-8−8i8i4i−4i-40000000040004i−4i000000000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i000-4-4000444i−4i4i−4i20000006-6-2000−2i2i00−6i6i00000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i000-4-4000444i−4i4i−4i2000000-66-2000−2i2i006i−6i00000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.