Finite Group Databasebeta

← Group #13135174

Character table — Group #13135174

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1244222344466612121212661212336666661212121212121212366666666666121212121212121212121212444488888888121212121212121224242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111-1-111-1-11111111-1-1-1-111-1-111-1-11111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ611111-1-111-1-11111111-1-1-1-111-1-111-1-11111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1ii−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ711111-1-111-1-11111111-1-1-1-111-1-111-1-11111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii
χ811111-1-111-1-11111111-1-1-1-111-1-111-1-11111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1−i−iii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i
χ911-1-11111-1-1-1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1i−ii−ii−ii−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-11111-1-1-1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1−ii−ii−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-11111-1-1-1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11i−ii−i−ii−ii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-11111-1-1-1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11−ii−iii−ii−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-11-1-11-111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111-1-111-1-1-1-11-1-111-1-1-1-11111i−i−iii−i−ii-111-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ1411-1-11-1-11-111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111-1-111-1-1-1-11-1-111-1-1-1-11111i−i−ii−iii−i1-1-11ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ1511-1-11-1-11-111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111-1-111-1-1-1-11-1-111-1-1-1-11111−iii−ii−i−ii1-1-11−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ1611-1-11-1-11-111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111-1-111-1-1-1-11-1-111-1-1-1-11111−iii−i−iii−i-111-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ1722222222222222222222222-1222-1-1-122-1-1-1-122-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222222222222-1222-1-1-122-1-1-1-122-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-2-2-2-200000000111111110000000000000000
χ192222222222222222222222-12-1-1-1222-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-1-1222-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ2122222-2-222-2-22222222-2-2-2-22-1-2-22-11122-1-111-2-2-12-1-21-1-11111-12-1-21-1-1-1-111112i2i−2i−2i00000000−i−i−i−iiiii0000000000000000
χ2222222-2-222-2-22222222-2-2-2-22-1-2-22-11122-1-111-2-2-12-1-21-1-11111-12-1-21-1-1-1-11111−2i−2i2i2i00000000iiii−i−i−i−i0000000000000000
χ2322222-2-222-2-22222222-2-2-2-2-1211-12-2-2-1-122-2-211-1-121-2-1-11111-1-121-2-1-1-1-11111000000002i2i−2i−2i0000000000000000−i−i−i−iiiii
χ2422222-2-222-2-22222222-2-2-2-2-1211-12-2-2-1-122-2-211-1-121-2-1-11111-1-121-2-1-1-1-1111100000000−2i−2i2i2i0000000000000000iiii−i−i−i−i
χ252222-22-22-2-22-2-22-2-2222-22-2222222-2-22222-2-2222-2-2-22-2-222-2-22-2-2-2222-2-222-2-2000000000000000000000000000000000000
χ262222-22-22-2-22-2-22-2-2222-22-22-1222-11122-1-11122-1-21-2-111-1-111-1-21-2-1-1-111-1-1110000000000003−33−33−33−30000000000000000
χ272222-22-22-2-22-2-22-2-2222-22-22-1222-11122-1-11122-1-21-2-111-1-111-1-21-2-1-1-111-1-111000000000000−33−33−33−330000000000000000
χ282222-22-22-2-22-2-22-2-2222-22-2-12-1-1-12-2-2-1-122-2-2-1-1-11-21211-1-111-11-212-1-111-1-1110000000000000000000000000000−i3i3−i3i3−i3i3−i3i3
χ292222-22-22-2-22-2-22-2-2222-22-2-12-1-1-12-2-2-1-122-2-2-1-1-11-21211-1-111-11-212-1-111-1-1110000000000000000000000000000i3−i3i3−i3i3−i3i3−i3
χ302222-2-222-22-2-2-22-2-222-22-2222-2-22222222222-2-22-2-22-2-2-2-2-2222-2-22-222-2-2-2-222000000000000000000000000000000000000
χ312222-2-222-22-2-2-22-2-222-22-222-1-2-22-1-1-122-1-1-1-1-2-2-1-21211111-1-1-1-2121-1-11111-1-1000000000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ322222-2-222-22-2-2-22-2-222-22-222-1-2-22-1-1-122-1-1-1-1-2-2-1-21211111-1-1-1-2121-1-11111-1-1000000000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ332222-2-222-22-2-2-22-2-222-22-22-1211-1222-1-1222211-11-2-1-21111-1-1-11-2-1-2-1-11111-1-100000000000000000000000000003−33−3−33−33
χ342222-2-222-22-2-2-22-2-222-22-22-1211-1222-1-1222211-11-2-1-21111-1-1-11-2-1-2-1-11111-1-10000000000000000000000000000−33−333−33−3
χ3522-2-22222-2-2-2222-2-2-2-222-2-22-1222-1-1-1-2-21111-2-2-12-12-1-1-1-1-1-1-1-1-21-21111111112-22-200000000-1-111-1-1110000000000000000
χ3622-2-22222-2-2-2222-2-2-2-222-2-22-1222-1-1-1-2-21111-2-2-12-12-1-1-1-1-1-1-1-1-21-2111111111-22-220000000011-1-111-1-10000000000000000
χ3722-2-22222-2-2-2222-2-2-2-222-2-2-12-1-1-122211-2-2-2-211-1-12-12-1-1-1-1-1-1-11-21-211111111000000002i−2i2i−2i0000000000000000−i−iii−i−iii
χ3822-2-22222-2-2-2222-2-2-2-222-2-2-12-1-1-122211-2-2-2-211-1-12-12-1-1-1-1-1-1-11-21-21111111100000000−2i2i−2i2i0000000000000000ii−i−iii−i−i
χ3922-2-22-2-22-222222-2-2-2-2-2-2222-1-2-22-111-2-211-1-122-12-1-21-1-11111-1-212-11111-1-1-1-12i−2i−2i2i00000000−i−iiiii−i−i0000000000000000
χ4022-2-22-2-22-222222-2-2-2-2-2-2222-1-2-22-111-2-211-1-122-12-1-21-1-11111-1-212-11111-1-1-1-1−2i2i2i−2i00000000ii−i−i−i−iii0000000000000000
χ4122-2-22-2-22-222222-2-2-2-2-2-222-1211-12-2-211-2-222-1-1-1-121-2-1-11111-11-2-121111-1-1-1-1000000002-2-220000000000000000-1-11111-1-1
χ4222-2-22-2-22-222222-2-2-2-2-2-222-1211-12-2-211-2-222-1-1-1-121-2-1-11111-11-2-121111-1-1-1-100000000-222-2000000000000000011-1-1-1-111
χ4322-2-2-22-2222-2-2-2222-2-22-2-22222222-2-2-2-2-2-222-2-22-2-2-22-2-222-2-22222-2-2-222-2-222000000000000000000000000000000000000
χ4422-2-2-22-2222-2-2-2222-2-22-2-222-1222-111-2-211-1-1-2-2-1-21-2-111-1-111-12-12111-1-111-1-10000000000003−3−333−3−330000000000000000
χ4522-2-2-22-2222-2-2-2222-2-22-2-222-1222-111-2-211-1-1-2-2-1-21-2-111-1-111-12-12111-1-111-1-1000000000000−333−3−333−30000000000000000
χ4622-2-2-22-2222-2-2-2222-2-22-2-22-12-1-1-12-2-211-2-22211-11-21211-1-111-1-12-1-211-1-111-1-100000000000000000000000000003−3−333−3−33
χ4722-2-2-22-2222-2-2-2222-2-22-2-22-12-1-1-12-2-211-2-22211-11-21211-1-111-1-12-1-211-1-111-1-10000000000000000000000000000−333−3−333−3
χ4822-2-2-2-2222-22-2-2222-2-2-222-222-2-22222-2-2-2-2-2-2222-2-22-2-2-2-2-222222-22-2-22222-2-2000000000000000000000000000000000000
χ4922-2-2-2-2222-22-2-2222-2-2-222-22-1-2-22-1-1-1-2-2111122-1-21211111-1-1-12-1-2-111-1-1-1-111000000000000−i3i3i3−i3i3−i3−i3i30000000000000000
χ5022-2-2-2-2222-22-2-2222-2-2-222-22-1-2-22-1-1-1-2-2111122-1-21211111-1-1-12-1-2-111-1-1-1-111000000000000i3−i3−i3i3−i3i3i3−i30000000000000000
χ5122-2-2-2-2222-22-2-2222-2-2-222-2-1211-122211-2-2-2-2-1-1-11-2-1-21111-1-1-1-121211-1-1-1-1110000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ5222-2-2-2-2222-22-2-2222-2-2-222-2-1211-122211-2-2-2-2-1-1-11-2-1-21111-1-1-1-121211-1-1-1-1110000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000
χ5444444-4-444-4-44444444-4-4-4-4-2-222-2-222-2-2-2-222221-2-22211-1-1-1-11-2-2221111-1-1-1-1000000000000000000000000000000000000
χ554444-44-44-4-44-4-44-4-4444-44-4-2-2-2-2-2-222-2-2-2-222-2-21222-2-1-111-1-11222-211-1-111-1-1000000000000000000000000000000000000
χ564444-4-444-44-4-4-44-4-444-44-44-2-222-2-2-2-2-2-2-2-2-2-222122-22-1-1-1-111122-2211-1-1-1-111000000000000000000000000000000000000
χ5744-4-44444-4-4-4444-4-4-4-444-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5844-4-44-4-44-444444-4-4-4-4-4-444-2-222-2-2222222-2-2-2-21-2-22211-1-1-1-1122-2-2-1-1-1-11111000000000000000000000000000000000000
χ5944-4-4-44-4444-4-4-4444-4-44-4-44-2-2-2-2-2-2222222-2-2221222-2-1-111-1-11-2-2-22-1-111-1-111000000000000000000000000000000000000
χ6044-4-4-4-4444-44-4-4444-4-4-444-4-2-222-2-2-2-2222222-2-2122-22-1-1-1-1111-2-22-2-1-11111-1-1000000000000000000000000000000000000
χ614-44i−4i000400000-4004i−4i00004400-4-4004i−4i4i−4i000040000000000-400004i−4i000000000000000000000000000000000000000000
χ624-44i−4i000400000-4004i−4i00004-200-42−2i32i34i−4i−2i2i23−2300-200000000−2i32i320000−2i2i000023−23000000000000000000000000000000000000
χ634-44i−4i000400000-4004i−4i00004-200-422i3−2i34i−4i−2i2i−232300-2000000002i3−2i320000−2i2i0000−2323000000000000000000000000000000000000
χ644-44i−4i000400000-4004i−4i0000-24−2i32i32-400−2i2i4i−4i0023−23-2000000−2i32i30020000−2i2i0023−2300000000000000000000000000000000000000
χ654-44i−4i000400000-4004i−4i0000-242i3−2i32-400−2i2i4i−4i00−2323-20000002i3−2i30020000−2i2i00−232300000000000000000000000000000000000000
χ664-44i−4i000400000-4004i−4i0000-2-2−2i32i322−2i32i3−2i2i−2i2i23−2323−23100003-3i3−i3i3−i3-10000i−i3i−3i−33−33000000000000000000000000000000000000
χ674-44i−4i000400000-4004i−4i0000-2-2−2i32i3222i3−2i3−2i2i−2i2i−232323−2310000-33i3−i3−i3i3-10000i−i−3i3i−333−3000000000000000000000000000000000000
χ684-44i−4i000400000-4004i−4i0000-2-22i3−2i322−2i32i3−2i2i−2i2i23−23−232310000-33−i3i3i3−i3-10000i−i−3i3i3−3−33000000000000000000000000000000000000
χ694-44i−4i000400000-4004i−4i0000-2-22i3−2i3222i3−2i3−2i2i−2i2i−2323−2323100003-3−i3i3−i3i3-10000i−i3i−3i3−33−3000000000000000000000000000000000000
χ704-4−4i4i000400000-400−4i4i00004400-4-400−4i4i−4i4i000040000000000-40000−4i4i000000000000000000000000000000000000000000
χ714-4−4i4i000400000-400−4i4i00004-200-42−2i32i3−4i4i2i−2i−232300-200000000−2i32i3200002i−2i0000−2323000000000000000000000000000000000000
χ724-4−4i4i000400000-400−4i4i00004-200-422i3−2i3−4i4i2i−2i23−2300-2000000002i3−2i3200002i−2i000023−23000000000000000000000000000000000000
χ734-4−4i4i000400000-400−4i4i0000-24−2i32i32-4002i−2i−4i4i00−2323-2000000−2i32i300200002i−2i00−232300000000000000000000000000000000000000
χ744-4−4i4i000400000-400−4i4i0000-242i3−2i32-4002i−2i−4i4i0023−23-20000002i3−2i300200002i−2i0023−2300000000000000000000000000000000000000
χ754-4−4i4i000400000-400−4i4i0000-2-2−2i32i322−2i32i32i−2i2i−2i−2323−2323100003-3i3−i3i3−i3-10000−ii−3i3i3−33−3000000000000000000000000000000000000
χ764-4−4i4i000400000-400−4i4i0000-2-2−2i32i3222i3−2i32i−2i2i−2i23−23−232310000-33i3−i3−i3i3-10000−ii3i−3i3−3−33000000000000000000000000000000000000
χ774-4−4i4i000400000-400−4i4i0000-2-22i3−2i322−2i32i32i−2i2i−2i−232323−2310000-33−i3i3i3−i3-10000−ii3i−3i−333−3000000000000000000000000000000000000
χ784-4−4i4i000400000-400−4i4i0000-2-22i3−2i3222i3−2i32i−2i2i−2i23−2323−23100003-3−i3i3−i3i3-10000−ii−3i3i−33−33000000000000000000000000000000000000
χ796666666-3666-3-3-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000000000002222000000000000-1-1-1-1-1-1-1-100000000
χ806666666-3666-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000-2-2-2-20000000000001111111100000000
χ8166666-6-6-36-6-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000000022-2-2000000000000-1-1-1-1111100000000
χ8266666-6-6-36-6-6-3-3-3-3-3-3-3333300000000000000000000000000000000000000000000-2-2220000000000001111-1-1-1-100000000
χ836666-66-6-3-6-6633-333-3-3-33-33000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ846666-66-6-3-6-6633-333-3-3-33-33000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ856666-6-66-3-66-633-333-3-33-33-3000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ866666-6-66-3-66-633-333-3-33-33-3000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ8766-6-6666-3-6-6-6-3-3-33333-3-333000000000000000000000000000000000000000000002i−2i2i−2i000000000000−i−iii−i−iii00000000
χ8866-6-6666-3-6-6-6-3-3-33333-3-33300000000000000000000000000000000000000000000−2i2i−2i2i000000000000ii−i−iii−i−i00000000
χ8966-6-66-6-6-3-666-3-3-3333333-3-3000000000000000000000000000000000000000000002i−2i−2i2i000000000000−i−iiiii−i−i00000000
χ9066-6-66-6-6-3-666-3-3-3333333-3-300000000000000000000000000000000000000000000−2i2i2i−2i000000000000ii−i−i−i−iii00000000
χ9166-6-6-66-6-366-633-3-3-333-333-30000000000000000000000000000000000000000000000000000000000003−3−333−3−3300000000
χ9266-6-6-66-6-366-633-3-3-333-333-3000000000000000000000000000000000000000000000000000000000000−333−3−333−300000000
χ9366-6-6-6-66-36-6633-3-3-3333-3-330000000000000000000000000000000000000000000000000000000000003−3−33−333−300000000
χ9466-6-6-6-66-36-6633-3-3-3333-3-33000000000000000000000000000000000000000000000000000000000000−333−33−3−3300000000
χ9512-1212i−12i000-6000−6i36i3663−63−6i6i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212i−12i000-60006i3−6i36−6363−6i6i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12−12i12i000-6000−6i36i36−63636i−6i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12−12i12i000-60006i3−6i3663−636i−6i00000000000000000000000000000000000000000000000000000000000000000000000000000000

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