Finite Group Databasebeta

← Group #13150691

Character table — Group #13150691

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12223444466612121212266121233666666121212123666666666661212121212121212121212121212444444442222244466666612121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
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
χ51111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1111111-1-1-1-111-1-11111-1-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-111
χ61111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1111111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111-1-1
χ71111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1111111-1-1-1-1-1-11111111-1-111-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ81111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1111-1-1-111111111-1-1-1-111-1-1-1-1-1-111
χ911111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-1-1-1-1-11111111111-1-1-11-11-1-11-1-1-111-1-111-1-11111-1-11-11-1
χ1011111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-1-1-1-1-111111111-1-111-1-11-11-1-11-1-1-1-11111-1-111-1-111-11-11
χ1111111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-111111-1-1-1-111-1-111-1-1-11-11
χ1211111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-111-111-111-1-111-1-111-1-1-1-1111-11-1
χ1311111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-11-11-111-1-11111-1-1-1-111-1-1-111-1
χ1411111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-1-111111-1-111-1-1-1-1-1-1111-1-11
χ1511111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11-11-1-1-1-111-1-1111111-1-11-1-11
χ1611111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-1-1111-1-1-111-1-1-1-11111-1-111-111-1
χ172222222222222222222222-122-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000220220000000000000000-1-1-1-1
χ182222222222222222222222-122-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000-2-20-2-200000000000000001111
χ19222222222222222222222-12-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000022220220000000-1-1-1-1000000-1-1-1-10000
χ20222222222222222222222-12-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000-2-2-2-20-2-20000000111100000011110000
χ212222222-2-22222222-2-2-2-2-22-122-1-1-12-2-2-2-2-1-2-211-1-11111-1-1-11122-1-1-1-1111100000000000220-2-20000000000000000-1-111
χ222222222-2-22222222-2-2-2-2-22-122-1-1-12-2-2-2-2-1-2-211-1-11111-1-1-11122-1-1-1-1111100000000000-2-2022000000000000000011-1-1
χ232222222-2-22222222-2-2-2-2-2-12-1-1222-11111-111-2-2-1-11111-122-2-2-1-1-1-1-1-11111000022220-2-200000001111000000-1-1-1-10000
χ242222222-2-22222222-2-2-2-2-2-12-1-1222-11111-111-2-2-1-11111-122-2-2-1-1-1-1-1-111110000-2-2-2-20220000000-1-1-1-100000011110000
χ2522222-2-222222-2-2-2-2-2-2-2222-122-1-1-122222-1-2-211-1-11111-111-1-1-2-21111-1-1-1-1000000000002-202-20000000000000000-11-11
χ2622222-2-222222-2-2-2-2-2-2-2222-122-1-1-122222-1-2-211-1-11111-111-1-1-2-21111-1-1-1-100000000000-220-2200000000000000001-11-1
χ2722222-2-222222-2-2-2-2-2-2-222-12-1-1222-1-1-1-1-1-111-2-2-1-11111-1-2-222111111-1-1-1-1000022-2-202-20000000-1-111000000-1-1110000
χ2822222-2-222222-2-2-2-2-2-2-222-12-1-1222-1-1-1-1-1-111-2-2-1-11111-1-2-222111111-1-1-1-10000-2-2220-22000000011-1-100000011-1-10000
χ2922222-2-2-2-2222-2-2-2-2222-2-22-122-1-1-12-2-2-2-2-122-1-1-1-1-1-1-1-1-11111-2-211111111000000000002-20-220000000000000000-111-1
χ3022222-2-2-2-2222-2-2-2-2222-2-22-122-1-1-12-2-2-2-2-122-1-1-1-1-1-1-1-1-11111-2-21111111100000000000-2202-200000000000000001-1-11
χ3122222-2-2-2-2222-2-2-2-2222-2-2-12-1-1222-11111-1-1-122-1-1-1-1-1-1-1-2-2-2-21111111111000022-2-20-22000000011-1-1000000-1-1110000
χ3222222-2-2-2-2222-2-2-2-2222-2-2-12-1-1222-11111-1-1-122-1-1-1-1-1-1-1-2-2-2-211111111110000-2-22202-20000000-1-11100000011-1-10000
χ3322-2-22002i−2i2-2-200000002i−2i222-22-2-2-22i2i−2i−2i200002-20000-2002i−2i0000002i2i−2i−2i2-22i−2i0000000000000000002-2002i−2i00000000
χ3422-2-22002i−2i2-2-200000002i−2i222-22-2-2-22i2i−2i−2i200002-20000-2002i−2i0000002i2i−2i−2i-22−2i2i000000000000000000-2200−2i2i00000000
χ3522-2-2200−2i2i2-2-20000000−2i2i222-22-2-2-2−2i−2i2i2i200002-20000-200−2i2i000000−2i−2i2i2i2-2−2i2i0000000000000000002-200−2i2i00000000
χ3622-2-2200−2i2i2-2-20000000−2i2i222-22-2-2-2−2i−2i2i2i200002-20000-200−2i2i000000−2i−2i2i2i-222i−2i000000000000000000-22002i−2i00000000
χ372-2-2222-200-2-2222-2-20000022-2-2-22-22000020000-2-2000022-2002-222-2-2000000002-22-2000000000000000000002-22-20000
χ382-2-2222-200-2-2222-2-20000022-2-2-22-22000020000-2-2000022-2002-222-2-200000000-22-2200000000000000000000-22-220000
χ392-2-2222-200-2-2222-2-200000-1211-22-2-1−i3i3−i3i3-1−i3i30011−i3−i3i3i3-12-200-11-1-111−i3i3−i3i300002-22-20000000000−i3i3−i3i3000000-11-110000
χ402-2-2222-200-2-2222-2-200000-1211-22-2-1−i3i3−i3i3-1−i3i30011−i3−i3i3i3-12-200-11-1-111−i3i3−i3i30000-22-220000000000i3−i3i3−i30000001-11-10000
χ412-2-2222-200-2-2222-2-200000-1211-22-2-1i3−i3i3−i3-1i3−i30011i3i3−i3−i3-12-200-11-1-111i3−i3i3−i300002-22-20000000000i3−i3i3−i3000000-11-110000
χ422-2-2222-200-2-2222-2-200000-1211-22-2-1i3−i3i3−i3-1i3−i30011i3i3−i3−i3-12-200-11-1-111i3−i3i3−i30000-22-220000000000−i3i3−i3i30000001-11-10000
χ432-2-222-2200-2-22-2-2220000022-2-2-22-22000020000-2-200002-2200-22-2-222000000002-2-22000000000000000000002-2-220000
χ442-2-222-2200-2-22-2-2220000022-2-2-22-22000020000-2-200002-2200-22-2-22200000000-222-200000000000000000000-222-20000
χ452-2-222-2200-2-22-2-22200000-1211-22-2-1−i3i3−i3i3-1i3−i30011i3i3−i3−i3-1-22001-111-1-1−i3i3−i3i300002-2-220000000000−i3i3i3−i3000000-111-10000
χ462-2-222-2200-2-22-2-22200000-1211-22-2-1−i3i3−i3i3-1i3−i30011i3i3−i3−i3-1-22001-111-1-1−i3i3−i3i30000-222-20000000000i3−i3−i3i30000001-1-110000
χ472-2-222-2200-2-22-2-22200000-1211-22-2-1i3−i3i3−i3-1−i3i30011−i3−i3i3i3-1-22001-111-1-1i3−i3i3−i300002-2-220000000000i3−i3−i3i3000000-111-10000
χ482-2-222-2200-2-22-2-22200000-1211-22-2-1i3−i3i3−i3-1−i3i30011−i3−i3i3i3-1-22001-111-1-1i3−i3i3−i30000-222-20000000000−i3i3i3−i30000001-1-110000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ504444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-2-21111-1-1-1-1000000000000000000000000000000000000
χ5144444-4-444444-4-4-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-222-1-1-1-11111000000000000000000000000000000000000
χ5244444-4-4-4-4444-4-4-4-4444-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5344-4-44004i−4i4-4-400000004i−4i4-24-4-222-44i4i−4i−4i-20000-220000200−2i2i000000−2i−2i2i2i000000000000000000000000000000000000
χ5444-4-44004i−4i4-4-400000004i−4i-24-224-4-42−2i−2i2i2i-20000-2200002004i−4i000000−2i−2i2i2i000000000000000000000000000000000000
χ5544-4-44004i−4i4-4-400000004i−4i-2-2-22-2222−2i−2i2i2i100001-13-33-3-100−2i2i003i−3i3i−3iii−i−i000000000000000000000000000000000000
χ5644-4-44004i−4i4-4-400000004i−4i-2-2-22-2222−2i−2i2i2i100001-1-33-33-100−2i2i00−3i3i−3i3iii−i−i000000000000000000000000000000000000
χ5744-4-4400−4i4i4-4-40000000−4i4i4-24-4-222-4−4i−4i4i4i-20000-2200002002i−2i0000002i2i−2i−2i000000000000000000000000000000000000
χ5844-4-4400−4i4i4-4-40000000−4i4i-24-224-4-422i2i−2i−2i-20000-220000200−4i4i0000002i2i−2i−2i000000000000000000000000000000000000
χ5944-4-4400−4i4i4-4-40000000−4i4i-2-2-22-22222i2i−2i−2i100001-13-33-3-1002i−2i00−3i3i−3i3i−i−iii000000000000000000000000000000000000
χ6044-4-4400−4i4i4-4-40000000−4i4i-2-2-22-22222i2i−2i−2i100001-1-33-33-1002i−2i003i−3i3i−3i−i−iii000000000000000000000000000000000000
χ614-44-440000-44-400000000044-44-4-44-4000040000-440000-400000000000000000000000000000000000000000000000000
χ624-44-440000-44-40000000004-2-4422-2-40000-200−2i32i32-2−2i32i32i3−2i3200000000000000000000000000000000000000000000000000
χ634-44-440000-44-40000000004-2-4422-2-40000-2002i3−2i32-22i3−2i3−2i32i3200000000000000000000000000000000000000000000000000
χ644-44-440000-44-4000000000-242-2-4-44223−23−2323-200002-200002000000000023−23−2323000000000000000000000000000000000000
χ654-44-440000-44-4000000000-242-2-4-442−232323−23-200002-2000020000000000−232323−23000000000000000000000000000000000000
χ664-44-440000-44-4000000000-2-22-222-2223−23−2323100−2i32i3-11i3−i3−i3i3-1000000−3i3i3i−3i−333−3000000000000000000000000000000000000
χ674-44-440000-44-4000000000-2-22-222-2223−23−23231002i3−2i3-11−i3i3i3−i3-10000003i−3i−3i3i−333−3000000000000000000000000000000000000
χ684-44-440000-44-4000000000-2-22-222-22−232323−23100−2i32i3-11i3−i3−i3i3-10000003i−3i−3i3i3−3−33000000000000000000000000000000000000
χ694-44-440000-44-4000000000-2-22-222-22−232323−231002i3−2i3-11−i3i3i3−i3-1000000−3i3i3i−3i3−3−33000000000000000000000000000000000000
χ704-4-4444-400-4-4444-4-4000004-2-4-42-2240000-20000220000-2-22004-4-2-2220000000000000000000000000000000000000000
χ714-4-4444-400-4-4444-4-400000-2-2222-22-2−2i32i3−2i32i31−2i32i300-1-1i3i3−i3−i31-2200-2211-1-1i3−i3i3−i3000000000000000000000000000000000000
χ724-4-4444-400-4-4444-4-400000-2-2222-22-22i3−2i32i3−2i312i3−2i300-1-1−i3−i3i3i31-2200-2211-1-1−i3i3−i3i3000000000000000000000000000000000000
χ734-4-444-4400-4-44-4-444000004-2-4-42-2240000-20000220000-22-200-4422-2-20000000000000000000000000000000000000000
χ744-4-444-4400-4-44-4-44400000-2-2222-22-2−2i32i3−2i32i312i3−2i300-1-1−i3−i3i3i312-2002-2-1-111i3−i3i3−i3000000000000000000000000000000000000
χ754-4-444-4400-4-44-4-44400000-2-2222-22-22i3−2i32i3−2i31−2i32i300-1-1i3i3−i3−i312-2002-2-1-111−i3i3−i3i3000000000000000000000000000000000000
χ766666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002222000020000200-1-10000-1-1-1-1-1-100000000
χ776666-36666-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-20000-20000-20011000011111100000000
χ786666-366-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000022-2-20000-20000200110000-1-1-1-11100000000
χ796666-366-6-6-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000-2-222000020000-200-1-100001111-1-100000000
χ806666-3-6-666-3-3-33333-633-3-30000000000000000000000000000000000000022220000-20000-200110000-1-111-1-100000000
χ816666-3-6-666-3-3-33333-633-3-300000000000000000000000000000000000000-2-2-2-2000020000200-1-1000011-1-11100000000
χ826666-3-6-6-6-6-3-3-333336-3-3330000000000000000000000000000000000000022-2-2000020000-200-1-10000-1-1111100000000
χ836666-3-6-6-6-6-3-3-333336-3-33300000000000000000000000000000000000000-2-2220000-2000020011000011-1-1-1-100000000
χ8466-6-6-3006i−6i-33333−3333−330−3i33i3−3i3i000000000000000000000000000000000000002-22i−2i000000000000−i3i30000-113−3−ii00000000
χ8566-6-6-3006i−6i-33333−3333−330−3i33i3−3i3i00000000000000000000000000000000000000-22−2i2i000000000000i3−i300001-1−33i−i00000000
χ8666-6-6-3006i−6i-333−3333−333303i3−3i3−3i3i000000000000000000000000000000000000002-22i−2i000000000000i3−i30000-11−33−ii00000000
χ8766-6-6-3006i−6i-333−3333−333303i3−3i3−3i3i00000000000000000000000000000000000000-22−2i2i000000000000−i3i300001-13−3i−i00000000
χ8866-6-6-300−6i6i-33333−3333−3303i3−3i33i−3i000000000000000000000000000000000000002-2−2i2i000000000000i3−i30000-113−3i−i00000000
χ8966-6-6-300−6i6i-33333−3333−3303i3−3i33i−3i00000000000000000000000000000000000000-222i−2i000000000000−i3i300001-1−33−ii00000000
χ9066-6-6-300−6i6i-333−3333−33330−3i33i33i−3i000000000000000000000000000000000000002-2−2i2i000000000000−i3i30000-11−33i−i00000000
χ9166-6-6-300−6i6i-333−3333−33330−3i33i33i−3i00000000000000000000000000000000000000-222i−2i000000000000i3−i300001-13−3−ii00000000
χ9212-1212-12-600006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-600006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-612-120066-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6-12120066-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000

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