Finite Group Databasebeta

← Group #13150689

Character table — Group #13150689

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222344446662661212121233666666121212121212121236666666666612121212121212121212121222444444224444446666661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-111-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-111
χ61111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-111-1-1-1-1-1-111-1111-1-1111111-1-1-1-111-1-1-1-111-1-1
χ71111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ81111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-1111-1-1-111-1-111111111-1-1-1-1-1-1-1-111
χ911111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111111111-1-11-1-11-1-11-11111-1-111-1-1-1-111-1-11-11-1
χ1011111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111111111-1-111-11-1-11-1-1111-1-11111-1-1-1-1-1-111-11-11
χ1111111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-11-11-111-11-1-111-1-1-1-1111111-1-1-11-11
χ1211111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-111-1111-111-1-1-1-1-111-1-11111-1-1111-11-1
χ1311111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111-11-11-111-1-111-1-111-1-111-1-1-111-1
χ1411111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-111-1-1-111111-1-1-1-111-1-1-1-1111-1-11
χ1511111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-11-11-11-1-1-1-11111-1-11111-1-11-1-11
χ1611111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1111-1-1-111-1-111-1-111-1-111-111-1
χ1722222222222222222222-1-1-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000022222200000000-1-1-1-1000000-1-1-1-10000
χ1822222222222222222222-1-1-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-200000000111100000011110000
χ192222222222222222222-1222-1-1-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222000000200200-1-10000-1-1-1-1-1-100000000
χ202222222222222222222-1222-1-1-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2000000-200-20011000011111100000000
χ212222222-2-2222-2-2-222-2-22-1-1-1222-122221111-1-2-211-1-11111-1-2-2-1-1-1-1-1-1111100002222-2-2000000001111000000-1-1-1-10000
χ222222222-2-2222-2-2-222-2-22-1-1-1222-122221111-1-2-211-1-11111-1-2-2-1-1-1-1-1-111110000-2-2-2-22200000000-1-1-1-100000011110000
χ232222222-2-2222-2-2-222-2-2-1222-1-1-12-1-1-1-1-2-2-2-2-111-2-2-1-11111-11122-1-1-1-1111122-2-2000000-200200-1-100001111-1-100000000
χ242222222-2-2222-2-2-222-2-2-1222-1-1-12-1-1-1-1-2-2-2-2-111-2-2-1-11111-11122-1-1-1-11111-2-222000000200-200110000-1-1-1-11100000000
χ2522222-2-222222-2-2-2-2-2222-1-1-1222-1-2-2-2-2-1-1-1-1-1-2-211-1-11111-122111111-1-1-1-1000022-2-22-200000000-1-111000000-1-1110000
χ2622222-2-222222-2-2-2-2-2222-1-1-1222-1-2-2-2-2-1-1-1-1-1-2-211-1-11111-122111111-1-1-1-10000-2-222-220000000011-1-100000011-1-10000
χ2722222-2-222222-2-2-2-2-222-1222-1-1-1211112222-111-2-2-1-11111-1-1-1-2-21111-1-1-1-12222000000-200-200-1-10000-1-1111100000000
χ2822222-2-222222-2-2-2-2-222-1222-1-1-1211112222-111-2-2-1-11111-1-1-1-2-21111-1-1-1-1-2-2-2-200000020020011000011-1-1-1-100000000
χ2922222-2-2-2-2222222-2-2-2-22-1-1-1222-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-21111111111000022-2-2-220000000011-1-1000000-1-1110000
χ3022222-2-2-2-2222222-2-2-2-22-1-1-1222-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-211111111110000-2-2222-200000000-1-11100000011-1-10000
χ3122222-2-2-2-2222222-2-2-2-2-1222-1-1-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-21111111122-2-2000000200-200-1-1000011-1-11100000000
χ3222222-2-2-2-2222222-2-2-2-2-1222-1-1-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-211111111-2-222000000-200200110000-1-111-1-100000000
χ332-22-22002i−2i-22-2000002i−2i222-22-2-2-200002i2i−2i−2i200002-20000-22i−2i0000002i2i−2i−2i2-22i−2i0000000000002-200002i−2i000000000000
χ342-22-22002i−2i-22-2000002i−2i222-22-2-2-200002i2i−2i−2i200002-20000-22i−2i0000002i2i−2i−2i-22−2i2i000000000000-220000−2i2i000000000000
χ352-22-22002i−2i-22-2000002i−2i-122-2-111-233−3−32i2i−2i−2i-1−i3i300-11−i3−i3i3i31−ii0033−3−3−i−iii2-22i−2i000000000000-110000−ii−i3i33−300000000
χ362-22-22002i−2i-22-2000002i−2i-122-2-111-233−3−32i2i−2i−2i-1−i3i300-11−i3−i3i3i31−ii0033−3−3−i−iii-22−2i2i0000000000001-10000i−ii3−i3−3300000000
χ372-22-22002i−2i-22-2000002i−2i-122-2-111-2−3−3332i2i−2i−2i-1i3−i300-11i3i3−i3−i31−ii00−3−333−i−iii2-22i−2i000000000000-110000−iii3−i3−3300000000
χ382-22-22002i−2i-22-2000002i−2i-122-2-111-2−3−3332i2i−2i−2i-1i3−i300-11i3i3−i3−i31−ii00−3−333−i−iii-22−2i2i0000000000001-10000i−i−i3i33−300000000
χ392-22-2200−2i2i-22-200000−2i2i222-22-2-2-20000−2i−2i2i2i200002-20000-2−2i2i000000−2i−2i2i2i2-2−2i2i0000000000002-20000−2i2i000000000000
χ402-22-2200−2i2i-22-200000−2i2i222-22-2-2-20000−2i−2i2i2i200002-20000-2−2i2i000000−2i−2i2i2i-222i−2i000000000000-2200002i−2i000000000000
χ412-22-2200−2i2i-22-200000−2i2i-122-2-111-233−3−3−2i−2i2i2i-1i3−i300-11i3i3−i3−i31i−i0033−3−3ii−i−i2-2−2i2i000000000000-110000i−ii3−i33−300000000
χ422-22-2200−2i2i-22-200000−2i2i-122-2-111-233−3−3−2i−2i2i2i-1i3−i300-11i3i3−i3−i31i−i0033−3−3ii−i−i-222i−2i0000000000001-10000−ii−i3i3−3300000000
χ432-22-2200−2i2i-22-200000−2i2i-122-2-111-2−3−333−2i−2i2i2i-1−i3i300-11−i3−i3i3i31i−i00−3−333ii−i−i2-2−2i2i000000000000-110000i−i−i3i3−3300000000
χ442-22-2200−2i2i-22-200000−2i2i-122-2-111-2−3−333−2i−2i2i2i-1−i3i300-11−i3−i3i3i31i−i00−3−333ii−i−i-222i−2i0000000000001-10000−iii3−i33−300000000
χ452-2-2222-200-2-220002-20022-2-2-2-2222-22-2000020000-2-200002002-22-22-2000000002-22-2000000000000000000002-22-20000
χ462-2-2222-200-2-220002-20022-2-2-2-2222-22-2000020000-2-200002002-22-22-200000000-22-2200000000000000000000-22-220000
χ472-2-2222-200-2-220002-2002-111-2-22-12-22-2−i3i3−i3i3-100−i3i311−i3i3−i3i3-100-11-11-11−i3i3−i3i300002-22-20000000000−i3i3−i3i3000000-11-110000
χ482-2-2222-200-2-220002-2002-111-2-22-12-22-2−i3i3−i3i3-100−i3i311−i3i3−i3i3-100-11-11-11−i3i3−i3i30000-22-220000000000i3−i3i3−i30000001-11-10000
χ492-2-2222-200-2-220002-2002-111-2-22-12-22-2i3−i3i3−i3-100i3−i311i3−i3i3−i3-100-11-11-11i3−i3i3−i300002-22-20000000000i3−i3i3−i3000000-11-110000
χ502-2-2222-200-2-220002-2002-111-2-22-12-22-2i3−i3i3−i3-100i3−i311i3−i3i3−i3-100-11-11-11i3−i3i3−i30000-22-220000000000−i3i3−i3i30000001-11-10000
χ512-2-222-2200-2-22000-220022-2-2-2-222-22-22000020000-2-20000200-22-22-22000000002-2-22000000000000000000002-2-220000
χ522-2-222-2200-2-22000-220022-2-2-2-222-22-22000020000-2-20000200-22-22-2200000000-222-200000000000000000000-222-20000
χ532-2-222-2200-2-22000-22002-111-2-22-1-22-22−i3i3−i3i3-100i3−i311i3−i3i3−i3-1001-11-11-1−i3i3−i3i300002-2-220000000000−i3i3i3−i3000000-111-10000
χ542-2-222-2200-2-22000-22002-111-2-22-1-22-22−i3i3−i3i3-100i3−i311i3−i3i3−i3-1001-11-11-1−i3i3−i3i30000-222-20000000000i3−i3−i3i30000001-1-110000
χ552-2-222-2200-2-22000-22002-111-2-22-1-22-22i3−i3i3−i3-100−i3i311−i3i3−i3i3-1001-11-11-1i3−i3i3−i300002-2-220000000000i3−i3−i3i3000000-111-10000
χ562-2-222-2200-2-22000-22002-111-2-22-1-22-22i3−i3i3−i3-100−i3i311−i3i3−i3i3-1001-11-11-1i3−i3i3−i30000-222-20000000000−i3i3i3−i30000001-1-110000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000
χ584444444-4-4444-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-222221222211-1-1-1-1122-2-21111-1-1-1-1000000000000000000000000000000000000
χ5944444-4-444444-4-4-4-4-444-2-2-2-2-2-2-2-22222-2-2-2-21222211-1-1-1-11-2-222-1-1-1-11111000000000000000000000000000000000000
χ6044444-4-4-4-4444444-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ6144-4-4400004-4-4000000044-44-44-4-40000000040000-440000-4000000000000000000000000000000000000000000000000
χ6244-4-4400004-4-400000004-22-2-44-42000023−23−2323-200002-2000020000000023−23−2323000000000000000000000000000000000000
χ6344-4-4400004-4-400000004-22-2-44-420000−232323−23-200002-20000200000000−232323−23000000000000000000000000000000000000
χ6444-4-4400004-4-40000000-24-442-22-423−23−23230000-200002-200002000023−23−23230000000000000000000000000000000000000000
χ6544-4-4400004-4-40000000-24-442-22-4−232323−230000-200002-2000020000−232323−230000000000000000000000000000000000000000
χ6644-4-4400004-4-40000000-2-22-22-22223−23−232323−23−232310000-11-333-3-10000−333−3−333−3000000000000000000000000000000000000
χ6744-4-4400004-4-40000000-2-22-22-22223−23−2323−232323−2310000-113-3-33-10000−333−33−3−33000000000000000000000000000000000000
χ6844-4-4400004-4-40000000-2-22-22-222−232323−2323−23−232310000-113-3-33-100003−3−33−333−3000000000000000000000000000000000000
χ6944-4-4400004-4-40000000-2-22-22-222−232323−23−232323−2310000-11-333-3-100003−3−333−3−33000000000000000000000000000000000000
χ704-44-44004i−4i-44-4000004i−4i4-2-224-4-420000−2i−2i2i2i-20000-22000024i−4i000000−2i−2i2i2i000000000000000000000000000000000000
χ714-44-44004i−4i-44-4000004i−4i-2-2-22-22222323−23−23−2i−2i2i2i1−2i32i3001-1i3i3−i3−i3-1−2i2i00−3−333ii−i−i000000000000000000000000000000000000
χ724-44-44004i−4i-44-4000004i−4i-2-2-22-2222−23−232323−2i−2i2i2i12i3−2i3001-1−i3−i3i3i3-1−2i2i0033−3−3ii−i−i000000000000000000000000000000000000
χ734-44-4400−4i4i-44-400000−4i4i4-2-224-4-4200002i2i−2i−2i-20000-2200002−4i4i0000002i2i−2i−2i000000000000000000000000000000000000
χ744-44-4400−4i4i-44-400000−4i4i-2-2-22-22222323−23−232i2i−2i−2i12i3−2i3001-1−i3−i3i3i3-12i−2i00−3−333−i−iii000000000000000000000000000000000000
χ754-44-4400−4i4i-44-400000−4i4i-2-2-22-2222−23−2323232i2i−2i−2i1−2i32i3001-1i3i3−i3−i3-12i−2i0033−3−3−i−iii000000000000000000000000000000000000
χ764-4-4444-400-4-440004-400-24-4-422-24-22-220000-20000220000-2004-4-22-220000000000000000000000000000000000000000
χ774-4-4444-400-4-440004-400-2-22222-2-2-22-22−2i32i3−2i32i3100−2i32i3-1-1i3−i3i3−i3100-221-11-1i3−i3i3−i3000000000000000000000000000000000000
χ784-4-4444-400-4-440004-400-2-22222-2-2-22-222i3−2i32i3−2i31002i3−2i3-1-1−i3i3−i3i3100-221-11-1−i3i3−i3i3000000000000000000000000000000000000
χ794-4-444-4400-4-44000-4400-24-4-422-242-22-20000-20000220000-200-442-22-20000000000000000000000000000000000000000
χ804-4-444-4400-4-44000-4400-2-22222-2-22-22-2−2i32i3−2i32i31002i3−2i3-1-1−i3i3−i3i31002-2-11-11i3−i3i3−i3000000000000000000000000000000000000
χ814-4-444-4400-4-44000-4400-2-22222-2-22-22-22i3−2i32i3−2i3100−2i32i3-1-1i3−i3i3−i31002-2-11-11−i3i3−i3i3000000000000000000000000000000000000
χ826666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000000220220000000000000000-1-1-1-1
χ836666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000000-2-20-2-200000000000000001111
χ846666-366-6-6-3-3-3-633-3-333000000000000000000000000000000000000000000000000000220-2-20000000000000000-1-111
χ856666-366-6-6-3-3-3-633-3-333000000000000000000000000000000000000000000000000000-2-2022000000000000000011-1-1
χ866666-3-6-666-3-3-3-63333-3-30000000000000000000000000000000000000000000000000002-202-20000000000000000-11-11
χ876666-3-6-666-3-3-3-63333-3-3000000000000000000000000000000000000000000000000000-220-2200000000000000001-11-1
χ886666-3-6-6-6-6-3-3-36-3-333330000000000000000000000000000000000000000000000000002-20-220000000000000000-111-1
χ896666-3-6-6-6-6-3-3-36-3-33333000000000000000000000000000000000000000000000000000-2202-200000000000000001-1-11
χ901212-12-12-60000-6660−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-60000-66606i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-60012i−12i6-6600000−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-600−12i12i6-66000006i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-612-120066-6000-66000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6-12120066-60006-6000000000000000000000000000000000000000000000000000000000000000000000000000000

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