Finite Group Databasebeta

← Group #13138879

Character table — Group #13138879

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order124423466688881212121224242424336612121212242424242424242436666612121212121224242424242424242424242422444466668888881212121212121212242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-11-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ51111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1
χ81111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111
χ911-1-1-1111-1-1ii−i−i-1-111ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1-1-1-111111-1-1ii−i−iiiii−i−i−i−i11-1-1i−i1111i−ii−i1-1ii−i−i-1-1-1-111-1-1ii−i−iii−i−i
χ1011-1-1-1111-1-1ii−i−i-1-111ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1-1-1-111111-1-1ii−i−iiiii−i−i−i−i1-1-11−ii11-1-1i−i−ii-11−i−iii-1-111-1-111ii−i−i−i−iii
χ1111-1-1-1111-1-1ii−i−i-1-111ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1-1-1-111111-1-1ii−i−iiiii−i−i−i−i-111-1−ii-1-111−iii−i-11−i−iii11-1-1-1-111−i−iiiii−i−i
χ1211-1-1-1111-1-1ii−i−i-1-111ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1-1-1-111111-1-1ii−i−iiiii−i−i−i−i-1-111i−i-1-1-1-1−ii−ii1-1ii−i−i111111-1-1−i−iii−i−iii
χ1311-1-1-1111-1-1−i−iii-1-111−i−iii1111-1-1-1-1−i−i−i−iiiii1-1-1-1-111111-1-1−i−iii−i−i−i−iiiii11-1-1−ii1111−ii−ii1-1−i−iii-1-1-1-111-1-1−i−iii−i−iii
χ1411-1-1-1111-1-1−i−iii-1-111−i−iii1111-1-1-1-1−i−i−i−iiiii1-1-1-1-111111-1-1−i−iii−i−i−i−iiiii1-1-11i−i11-1-1−iii−i-11ii−i−i-1-111-1-111−i−iiiii−i−i
χ1511-1-1-1111-1-1−i−iii-1-111−i−iii1111-1-1-1-1−i−i−i−iiiii1-1-1-1-111111-1-1−i−iii−i−i−i−iiiii-111-1i−i-1-111i−i−ii-11ii−i−i11-1-1-1-111ii−i−i−i−iii
χ1611-1-1-1111-1-1−i−iii-1-111−i−iii1111-1-1-1-1−i−i−i−iiiii1-1-1-1-111111-1-1−i−iii−i−i−i−iiiii-1-111−ii-1-1-1-1i−ii−i1-1−i−iii111111-1-1ii−i−iii−i−i
χ1722222222222222222222222-12-122-1-122-1-122-1-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-1-102020000-1-1002200000000-1-100000000-1-1-1-1
χ1822222222222222222222222-12-122-1-122-1-122-1-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-1-10-20-200001100-2-20000000011000000001111
χ192222222222222222222222-12-12-1-122-1-122-1-122-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-1202000-1-1002200000000-1-1000000-1-1-1-10000
χ202222222222222222222222-12-12-1-122-1-122-1-122-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-1-20-20001100-2-2000000001100000011110000
χ212222222222-2-2-2-22222-2-2-2-22-12-122-1-1-2-211-2-211-12-1-1-1-12-1-1-1-1-1-21-211111111102020000-1-100-2-200000000-1-1000000001111
χ222222222222-2-2-2-22222-2-2-2-22-12-122-1-1-2-211-2-211-12-1-1-1-12-1-1-1-1-1-21-21111111110-20-20000110022000000001100000000-1-1-1-1
χ232222222222-2-2-2-22222-2-2-2-2-12-12-1-12211-2-211-2-2-1-12-1-1-1-12-1-1-1-11-21-211111111202000-1-100-2-200000000-1-100000011110000
χ242222222222-2-2-2-22222-2-2-2-2-12-12-1-12211-2-211-2-2-1-12-1-1-1-12-1-1-1-11-21-211111111-20-20001100220000000011000000-1-1-1-10000
χ252222-22-22-2-22-22-222-2-22-22-22222222222-2-222-2-22-2-2-2-22-2-2-2-222-22-2222-2-222-2-2000000000000000000000000000000000000
χ262222-22-22-2-22-22-222-2-22-22-22-12-122-1-122112211-1-2111-1-2111-1-1-2-1-2-1-1-111-1-11100000000−i3i3000000000000−i3i300000000−i3i3−i3i3
χ272222-22-22-2-22-22-222-2-22-22-22-12-122-1-122112211-1-2111-1-2111-1-1-2-1-2-1-1-111-1-11100000000i3−i3000000000000i3−i300000000i3−i3i3−i3
χ282222-22-22-2-22-22-222-2-22-22-2-12-12-1-122-1-1-2-2-1-1-2-2-11-211-11-211-1-11212-1-111-1-111000000−i3i3000000000000−i3i3000000−i3i3−i3i30000
χ292222-22-22-2-22-22-222-2-22-22-2-12-12-1-122-1-1-2-2-1-1-2-2-11-211-11-211-1-11212-1-111-1-111000000i3−i3000000000000i3−i3000000i3−i3i3−i30000
χ302222-22-22-2-2-22-2222-2-2-22-2222222222-2-222-2-2222-2-2-2-22-2-2-2-2222-22-2-2-222-2-222000000000000000000000000000000000000
χ312222-22-22-2-2-22-2222-2-2-22-222-12-122-1-1-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1212111-1-111-1-100000000−i3i3000000000000−i3i300000000i3−i3i3−i3
χ322222-22-22-2-2-22-2222-2-2-22-222-12-122-1-1-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1212111-1-111-1-100000000i3−i3000000000000i3−i300000000−i3i3−i3i3
χ332222-22-22-2-2-22-2222-2-2-22-22-12-12-1-12211221122-11-211-11-211-1-1-1-2-1-211-1-111-1-1000000−i3i3000000000000−i3i3000000i3−i3i3−i30000
χ342222-22-22-2-2-22-2222-2-2-22-22-12-12-1-12211221122-11-211-11-211-1-1-1-2-1-211-1-111-1-1000000i3−i3000000000000i3−i3000000−i3i3−i3i30000
χ3522-2-222-22222i−2i−2i2i-2-2-2-22i−2i−2i2i2222-2-2-2-22i2i−2i−2i−2i−2i2i2i222222-2-2-2-2-2-2−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ3622-2-222-22222i−2i−2i2i-2-2-2-22i−2i−2i2i2-12-1-2-2112i2iii−2i−2i−i−i-12-1-1-1-1-211111−2i−i2ii−i−iiiii−i−i00000000−i3i3000000000000i3−i3000000003−3−33
χ3722-2-222-22222i−2i−2i2i-2-2-2-22i−2i−2i2i2-12-1-2-2112i2iii−2i−2i−i−i-12-1-1-1-1-211111−2i−i2ii−i−iiiii−i−i00000000i3−i3000000000000−i3i300000000−333−3
χ3822-2-222-22222i−2i−2i2i-2-2-2-22i−2i−2i2i-12-1211-2-2−i−i−2i−2iii2i2i-1-12-1-1-11-21111i2i−i−2i−i−iiiii−i−i000000−i3i3000000000000i3−i30000003−3−330000
χ3922-2-222-22222i−2i−2i2i-2-2-2-22i−2i−2i2i-12-1211-2-2−i−i−2i−2iii2i2i-1-12-1-1-11-21111i2i−i−2i−i−iiiii−i−i000000i3−i3000000000000−i3i3000000−333−30000
χ4022-2-222-2222−2i2i2i−2i-2-2-2-2−2i2i2i−2i2222-2-2-2-2−2i−2i2i2i2i2i−2i−2i222222-2-2-2-2-2-22i−2i−2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4122-2-222-2222−2i2i2i−2i-2-2-2-2−2i2i2i−2i2-12-1-2-211−2i−2i−i−i2i2iii-12-1-1-1-1-2111112ii−2i−iii−i−i−i−iii00000000−i3i3000000000000i3−i300000000−333−3
χ4222-2-222-2222−2i2i2i−2i-2-2-2-2−2i2i2i−2i2-12-1-2-211−2i−2i−i−i2i2iii-12-1-1-1-1-2111112ii−2i−iii−i−i−i−iii00000000i3−i3000000000000−i3i3000000003−3−33
χ4322-2-222-2222−2i2i2i−2i-2-2-2-2−2i2i2i−2i-12-1211-2-2ii2i2i−i−i−2i−2i-1-12-1-1-11-21111−i−2ii2iii−i−i−i−iii000000−i3i3000000000000i3−i3000000−333−30000
χ4422-2-222-2222−2i2i2i−2i-2-2-2-2−2i2i2i−2i-12-1211-2-2ii2i2i−i−i−2i−2i-1-12-1-1-11-21111−i−2ii2iii−i−i−i−iii000000i3−i3000000000000−i3i30000003−3−330000
χ4522-2-2-2222-2-22i2i−2i−2i-2-2222i2i−2i−2i2-12-1-2-2112i2i−i−i−2i−2iii-1-2111-12-1-1-1112i−i−2ii−i−i−i−iiiii020-20000-1-1002i−2i000000001100000000−i−iii
χ4622-2-2-2222-2-22i2i−2i−2i-2-2222i2i−2i−2i2-12-1-2-2112i2i−i−i−2i−2iii-1-2111-12-1-1-1112i−i−2ii−i−i−i−iiiii0-20200001100−2i2i00000000-1-100000000ii−i−i
χ4722-2-2-2222-2-22i2i−2i−2i-2-2222i2i−2i−2i-12-1211-2-2−i−i2i2iii−2i−2i-11-211-1-12-1-111−i2ii−2i−i−i−i−iiiii20-2000-1-1002i−2i0000000011000000−i−iii0000
χ4822-2-2-2222-2-22i2i−2i−2i-2-2222i2i−2i−2i-12-1211-2-2−i−i2i2iii−2i−2i-11-211-1-12-1-111−i2ii−2i−i−i−i−iiiii-2020001100−2i2i00000000-1-1000000ii−i−i0000
χ4922-2-2-2222-2-2−2i−2i2i2i-2-222−2i−2i2i2i2-12-1-2-211−2i−2iii2i2i−i−i-1-2111-12-1-1-111−2ii2i−iiiii−i−i−i−i020-20000-1-100−2i2i000000001100000000ii−i−i
χ5022-2-2-2222-2-2−2i−2i2i2i-2-222−2i−2i2i2i2-12-1-2-211−2i−2iii2i2i−i−i-1-2111-12-1-1-111−2ii2i−iiiii−i−i−i−i0-202000011002i−2i00000000-1-100000000−i−iii
χ5122-2-2-2222-2-2−2i−2i2i2i-2-222−2i−2i2i2i-12-1211-2-2ii−2i−2i−i−i2i2i-11-211-1-12-1-111i−2i−i2iiiii−i−i−i−i20-2000-1-100−2i2i0000000011000000ii−i−i0000
χ5222-2-2-2222-2-2−2i−2i2i2i-2-222−2i−2i2i2i-12-1211-2-2ii−2i−2i−i−i2i2i-11-211-1-12-1-111i−2i−i2iiiii−i−i−i−i-20200011002i−2i00000000-1-1000000−i−iii0000
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2111-2-21111-2-2-2-211111111000000000000000000000000000000000000
χ544444444444-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2111-2-211112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-44-44-4-44-44-444-4-44-44-4-2-2-2-2-2-2-2-2-2-222-2-222122-1-1122-1-1112-22-211-1-111-1-1000000000000000000000000000000000000
χ564444-44-44-4-4-44-4444-4-4-44-44-2-2-2-2-2-2-2-222-2-222-2-2122-1-1122-1-111-22-22-1-111-1-111000000000000000000000000000000000000
χ5744-4-444-44444i−4i−4i4i-4-4-4-44i−4i−4i4i-2-2-2-22222−2i−2i2i2i2i2i−2i−2i1-2-211122-1-1-1-12i−2i−2i2iii−i−i−i−iii000000000000000000000000000000000000
χ5844-4-444-4444−4i4i4i−4i-4-4-4-4−4i4i4i−4i-2-2-2-222222i2i−2i−2i−2i−2i2i2i1-2-211122-1-1-1-1−2i2i2i−2i−i−iiiii−i−i000000000000000000000000000000000000
χ5944-4-4-4444-4-44i4i−4i−4i-4-4444i4i−4i−4i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i122-1-11-2-211-1-1−2i−2i2i2iiiii−i−i−i−i000000000000000000000000000000000000
χ6044-4-4-4444-4-4−4i−4i4i4i-4-444−4i−4i4i4i-2-2-2-222222i2i2i2i−2i−2i−2i−2i122-1-11-2-211-1-12i2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000
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χ644-44i−4i040-40000004i−4i000000-242-4−2i2i4i−4i−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ1300-2000020000−2i2i0000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000000000000000
χ654-44i−4i040-40000004i−4i000000-242-4−2i2i4i−4i2ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ1300-2000020000−2i2i00002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000000000000000
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χ704-4−4i4i040-4000000−4i4i00000044-4-4−4i4i−4i4i0000000040000-40000−4i4i000000000000000000000000000000000000000000000000
χ714-4−4i4i040-4000000−4i4i0000004-2-42−4i4i2i−2i00−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13-20000200002i−2i000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000
χ724-4−4i4i040-4000000−4i4i0000004-2-42−4i4i2i−2i002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13-20000200002i−2i0000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
χ734-4−4i4i040-4000000−4i4i000000-242-42i−2i−4i4i2ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ2300-20000200002i−2i00002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000000000
χ744-4−4i4i040-4000000−4i4i000000-242-42i−2i−4i4i−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ2300-20000200002i−2i0000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000000000
χ754-4−4i4i040-4000000−4i4i000000-2-2222i−2i2i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ131003-3-100−3i3i−ii0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000000
χ764-4−4i4i040-4000000−4i4i000000-2-2222i−2i2i−2i2ζ5−2ζ13−2ζ5+2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ23−2ζ5+2ζ132ζ5−2ζ13100-33-1003i−3i−ii0000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000000
χ774-4−4i4i040-4000000−4i4i000000-2-2222i−2i2i−2i−2ζ5+2ζ132ζ5−2ζ13−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ232ζ5−2ζ13−2ζ5+2ζ13100-33-1003i−3i−ii0000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000000
χ784-4−4i4i040-4000000−4i4i000000-2-2222i−2i2i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ232ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ131003-3-100−3i3i−ii0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000000
χ7966666-36-3-3-36666-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000220000000022-1-1-1-10000-1-1-1-100000000
χ8066666-36-3-3-36666-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000-2-200000000-2-211110000111100000000
χ8166666-36-3-3-3-6-6-6-6-3-3-3-33333000000000000000000000000000000000000000000002200000000-2-2-1-1-1-10000111100000000
χ8266666-36-3-3-3-6-6-6-6-3-3-3-3333300000000000000000000000000000000000000000000-2-2000000002211110000-1-1-1-100000000
χ836666-6-3-6-3336-66-6-3-333-33-33000000000000000000000000000000000000000000000000000000003−33−300003−33−300000000
χ846666-6-3-6-3336-66-6-3-333-33-3300000000000000000000000000000000000000000000000000000000−33−330000−33−3300000000
χ856666-6-3-6-333-66-66-3-3333-33-3000000000000000000000000000000000000000000000000000000003−33−30000−33−3300000000
χ866666-6-3-6-333-66-66-3-3333-33-300000000000000000000000000000000000000000000000000000000−33−3300003−33−300000000
χ8766-6-66-3-6-3-3-36i−6i−6i6i3333−3i3i3i−3i00000000000000000000000000000000000000000000000000000000−i3i3i3−i30000−333−300000000
χ8866-6-66-3-6-3-3-36i−6i−6i6i3333−3i3i3i−3i00000000000000000000000000000000000000000000000000000000i3−i3−i3i300003−3−3300000000
χ8966-6-66-3-6-3-3-3−6i6i6i−6i33333i−3i−3i3i00000000000000000000000000000000000000000000000000000000−i3i3i3−i300003−3−3300000000
χ9066-6-66-3-6-3-3-3−6i6i6i−6i33333i−3i−3i3i00000000000000000000000000000000000000000000000000000000i3−i3−i3i30000−333−300000000
χ9166-6-6-6-36-3336i6i−6i−6i33-3-3−3i−3i3i3i000000000000000000000000000000000000000000002i−2i000000002-2−i−iii0000-1-11100000000
χ9266-6-6-6-36-3336i6i−6i−6i33-3-3−3i−3i3i3i00000000000000000000000000000000000000000000−2i2i00000000-22ii−i−i000011-1-100000000
χ9366-6-6-6-36-333−6i−6i6i6i33-3-33i3i−3i−3i000000000000000000000000000000000000000000002i−2i00000000-22−i−iii000011-1-100000000
χ9466-6-6-6-36-333−6i−6i6i6i33-3-33i3i−3i−3i00000000000000000000000000000000000000000000−2i2i000000002-2ii−i−i0000-1-11100000000
χ9512-1212i−12i0-606−6i36i30000−6i6i63−6300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212i−12i0-6066i3−6i30000−6i6i−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12−12i12i0-606−6i36i300006i−6i−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12−12i12i0-6066i3−6i300006i−6i63−6300000000000000000000000000000000000000000000000000000000000000000000000000000000

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