Finite Group Databasebeta

← Group #13150853

Character table — Group #13150853

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12222234466666664121212123366666612121212366666666666121212121212121212121212121222444444224444446666661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-11-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-11-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-11-11-11111-1-1-1-1-1-111-1-1111-11-1
χ61111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-11-11111111-1-1-1-1-1-111-1-1-11-11
χ71111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11-11-1-1-1-1-1-1111111-1-111-11-11
χ81111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-11-1-1-1-1-1111111-1-111-1-11-11-1
χ91111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-111-1-11111-1-11-1-11
χ101111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-111-11-1-1-111-111-1-11111-1-1-1-1-1-111-111-1
χ111111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-111-1-11-111-111-1-1-111-1-1-1-1111111-1-1-111-1
χ121111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-11111-1-111-1-1-1-1111-1-11
χ131111-1-11-1-11-1-1-1-1111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-1111111-1-111-1-1-111-111-1-111-1-111-1-11111-1-1-1-111-1-1
χ141111-1-11-1-11-1-1-1-1111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-11111-1-111
χ151111-1-11-1-11-1-1-1-1111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-111
χ161111-1-11-1-11-1-1-1-1111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-11111-1-111-1-1111-1-1111-1-1-1-111-1-111-1-1-1-1111111-1-1
χ172222222222222222222222-12-1-1-122-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100002222020200000000-1-10000-1-1-1-1-1-10000
χ182222222222222222222222-12-1-1-122-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20-20-2000000001100001111110000
χ19222222222222222222222-12-1222-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000022220000000000000000-1-1-1-1
χ20222222222222222222222-12-1222-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000000001111
χ212222222-2-22222222-2-2-2-2-22-12-1-1-1221111-122-1-1-1-1-1-1-1-1-111-2-2-2-211111111000022220-20-200000000110000-1-111-1-10000
χ222222222-2-22222222-2-2-2-2-22-12-1-1-1221111-122-1-1-1-1-1-1-1-1-111-2-2-2-2111111110000-2-2-2-2020200000000-1-1000011-1-1110000
χ232222222-2-22222222-2-2-2-2-2-12-1222-1-1-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-21111111111110000000000002-22-20000000000000000-11-11
χ242222222-2-22222222-2-2-2-2-2-12-1222-1-1-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-2111111111111000000000000-22-2200000000000000001-11-1
χ252222-2-22222-2-2-2-222-222-2-22-12-1-1-122-1-1-1-1-1-2-211-1-11111-11122-2-2-1-1-1-11111000022-2-20-20200000000110000-1-1-1-1110000
χ262222-2-22222-2-2-2-222-222-2-22-12-1-1-122-1-1-1-1-1-2-211-1-11111-11122-2-2-1-1-1-111110000-2-222020-200000000-1-100001111-1-10000
χ272222-2-22222-2-2-2-222-222-2-2-12-1222-1-12222-111-2-2-1-11111-1-2-2-1-111-1-1-1-111110000000000002-2-220000000000000000-111-1
χ282222-2-22222-2-2-2-222-222-2-2-12-1222-1-12222-111-2-2-1-11111-1-2-2-1-111-1-1-1-11111000000000000-222-200000000000000001-1-11
χ292222-2-22-2-22-2-2-2-2222-2-2222-12-1-1-1221111-1-2-211-1-11111-1-1-1-2-2221111-1-1-1-1000022-2-2020-200000000-1-10000-1-111110000
χ302222-2-22-2-22-2-2-2-2222-2-2222-12-1-1-1221111-1-2-211-1-11111-1-1-1-2-2221111-1-1-1-10000-2-2220-2020000000011000011-1-1-1-10000
χ312222-2-22-2-22-2-2-2-2222-2-222-12-1222-1-1-2-2-2-2-111-2-2-1-11111-12211-1-11111-1-1-1-100000000000022-2-20000000000000000-1-111
χ322222-2-22-2-22-2-2-2-2222-2-222-12-1222-1-1-2-2-2-2-111-2-2-1-11111-12211-1-11111-1-1-1-1000000000000-2-222000000000000000011-1-1
χ3322-2-20022i−2i20000-2-202i−2i0022-22-2-22-22i2i−2i−2i200002-20000-2002i−2i002i2i−2i−2i00002-22i−2i0000000000002-200002i−2i000000000000
χ3422-2-20022i−2i20000-2-202i−2i0022-22-2-22-22i2i−2i−2i200002-20000-2002i−2i002i2i−2i−2i0000-22−2i2i000000000000-220000−2i2i000000000000
χ3522-2-2002−2i2i20000-2-20−2i2i0022-22-2-22-2−2i−2i2i2i200002-20000-200−2i2i00−2i−2i2i2i00002-2−2i2i0000000000002-20000−2i2i000000000000
χ3622-2-2002−2i2i20000-2-20−2i2i0022-22-2-22-2−2i−2i2i2i200002-20000-200−2i2i00−2i−2i2i2i0000-222i−2i000000000000-2200002i−2i000000000000
χ372-22-22-2200-222-2-2-2200000222-22-2-2-2000022-22-2-2222-2-2-20000000000000000002i−2i2i−2i0000000000000000002i−2i002i−2i0000
χ382-22-22-2200-222-2-2-2200000222-22-2-2-2000022-22-2-2222-2-2-2000000000000000000−2i2i−2i2i000000000000000000−2i2i00−2i2i0000
χ392-22-22-2200-222-2-2-22000002-121-11-2-23−33−3-12-2-111-1-1-11113−300003−33−333−3−300002i−2i2i−2i000000000000−i3i30000−ii−i3i3−ii0000
χ402-22-22-2200-222-2-2-22000002-121-11-2-23−33−3-12-2-111-1-1-11113−300003−33−333−3−30000−2i2i−2i2i000000000000i3−i30000i−ii3−i3i−i0000
χ412-22-22-2200-222-2-2-22000002-121-11-2-2−33−33-12-2-111-1-1-1111−330000−33−33−3−33300002i−2i2i−2i000000000000i3−i30000−iii3−i3−ii0000
χ422-22-22-2200-222-2-2-22000002-121-11-2-2−33−33-12-2-111-1-1-1111−330000−33−33−3−3330000−2i2i−2i2i000000000000−i3i30000i−i−i3i3i−i0000
χ432-22-2-22200-2-2-222-2200000222-22-2-2-200002-22-22-22-2-222-20000000000000000002i−2i−2i2i0000000000000000002i−2i00−2i2i0000
χ442-22-2-22200-2-2-222-2200000222-22-2-2-200002-22-22-22-2-222-2000000000000000000−2i2i2i−2i000000000000000000−2i2i002i−2i0000
χ452-22-2-22200-2-2-222-22000002-121-11-2-23−33−3-1-221-11-111-1-11−3300003−33−3−3−33300002i−2i−2i2i000000000000i3−i30000−ii−i3i3i−i0000
χ462-22-2-22200-2-2-222-22000002-121-11-2-23−33−3-1-221-11-111-1-11−3300003−33−3−3−3330000−2i2i2i−2i000000000000−i3i30000i−ii3−i3−ii0000
χ472-22-2-22200-2-2-222-22000002-121-11-2-2−33−33-1-221-11-111-1-113−30000−33−3333−3−300002i−2i−2i2i000000000000−i3i30000−iii3−i3i−i0000
χ482-22-2-22200-2-2-222-22000002-121-11-2-2−33−33-1-221-11-111-1-113−30000−33−3333−3−30000−2i2i2i−2i000000000000i3−i30000i−i−i3i3−ii0000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ504444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ514444-4-44444-4-4-4-444-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-2221111-1-1-1-1000000000000000000000000000000000000
χ524444-4-44-4-44-4-4-4-4444-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-2-2-1-1-1-11111000000000000000000000000000000000000
χ5344-4-40044i−4i40000-4-404i−4i004-2-4-2224-4−2i−2i2i2i-20000-2200002004i−4i00−2i−2i2i2i0000000000000000000000000000000000000000
χ5444-4-40044i−4i40000-4-404i−4i00-2424-4-4-224i4i−4i−4i-20000-220000200−2i2i00−2i−2i2i2i0000000000000000000000000000000000000000
χ5544-4-40044i−4i40000-4-404i−4i00-2-22-222-22−2i−2i2i2i100001-13-33-3-100−2i2i00ii−i−i3i−3i3i−3i000000000000000000000000000000000000
χ5644-4-40044i−4i40000-4-404i−4i00-2-22-222-22−2i−2i2i2i100001-1-33-33-100−2i2i00ii−i−i−3i3i−3i3i000000000000000000000000000000000000
χ5744-4-4004−4i4i40000-4-40−4i4i004-2-4-2224-42i2i−2i−2i-20000-220000200−4i4i002i2i−2i−2i0000000000000000000000000000000000000000
χ5844-4-4004−4i4i40000-4-40−4i4i00-2424-4-4-22−4i−4i4i4i-20000-2200002002i−2i002i2i−2i−2i0000000000000000000000000000000000000000
χ5944-4-4004−4i4i40000-4-40−4i4i00-2-22-222-222i2i−2i−2i100001-13-33-3-1002i−2i00−i−iii−3i3i−3i3i000000000000000000000000000000000000
χ6044-4-4004−4i4i40000-4-40−4i4i00-2-22-222-222i2i−2i−2i100001-1-33-33-1002i−2i00−i−iii3i−3i3i−3i000000000000000000000000000000000000
χ614-44-44-4400-444-4-4-4400000-24-2-44-4220000-2-224-42-2-2-222200000000000000000000000000000000000000000000000000
χ624-44-44-4400-444-4-4-4400000-2-2-22-222223−2323−231-22-22-1111-1-1-123−230000−33−33−3−333000000000000000000000000000000000000
χ634-44-44-4400-444-4-4-4400000-2-2-22-2222−2323−23231-22-22-1111-1-1-1−232300003−33−333−3−3000000000000000000000000000000000000
χ644-44-4-44400-4-4-444-4400000-24-2-44-4220000-22-2-442-222-2-2200000000000000000000000000000000000000000000000000
χ654-44-4-44400-4-4-444-4400000-2-2-22-222223−2323−2312-22-2-11-1-111-1−23230000−33−3333−3−3000000000000000000000000000000000000
χ664-44-4-44400-4-4-444-4400000-2-2-22-2222−2323−232312-22-2-11-1-111-123−2300003−33−3−3−333000000000000000000000000000000000000
χ674-4-4400400-400004-40000044-4-4-44-44000040000-4-40000400000000000000000000000000000000000000000000000000
χ684-4-4400400-400004-4000004-2-422-2-44−2i32i32i3−2i3-20000220000-2000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ694-4-4400400-400004-4000004-2-422-2-442i3−2i3−2i32i3-20000220000-20000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ704-4-4400400-400004-400000-242-4-442-20000-20000220000-20000−2i32i30000−2i32i32i3−2i3000000000000000000000000000000000000
χ714-4-4400400-400004-400000-242-4-442-20000-20000220000-200002i3−2i300002i3−2i3−2i32i3000000000000000000000000000000000000
χ724-4-4400400-400004-400000-2-2222-22-2−2i32i32i3−2i310000-1-13-3-33100002i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000
χ734-4-4400400-400004-400000-2-2222-22-2−2i32i32i3−2i310000-1-1-333-310000−2i32i3i3−i3−i3i3i3−i3−i3i3000000000000000000000000000000000000
χ744-4-4400400-400004-400000-2-2222-22-22i3−2i3−2i32i310000-1-13-3-3310000−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000000000
χ754-4-4400400-400004-400000-2-2222-22-22i3−2i3−2i32i310000-1-1-333-3100002i3−2i3−i3i3i3−i3−i3i3i3−i3000000000000000000000000000000000000
χ76666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002222000020200000-1-1-1-100-1-1-1-10000000000
χ77666666-366-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-20000-20-20000011110011110000000000
χ78666666-3-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000022-2-2000020-200000-1-1-1-10011110000000000
χ79666666-3-6-6-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000-2-2220000-20200000111100-1-1-1-10000000000
χ806666-6-6-366-33333-3-3-6-3-3330000000000000000000000000000000000000022220000-20-200000-1-11100-1-1110000000000
χ816666-6-6-366-33333-3-3-6-3-33300000000000000000000000000000000000000-2-2-2-200002020000011-1-10011-1-10000000000
χ826666-6-6-3-6-6-33333-3-3633-3-30000000000000000000000000000000000000022-2-20000-20200000-1-1110011-1-10000000000
χ836666-6-6-3-6-6-33333-3-3633-3-300000000000000000000000000000000000000-2-222000020-20000011-1-100-1-1110000000000
χ8466-6-600-36i−6i-3−3i33i3−3i33i3330−3i3i33−33000000000000000000000000000000000000002-22i−2i000000000000-11−i3i300−ii3−30000000000
χ8566-6-600-36i−6i-3−3i33i3−3i33i3330−3i3i33−3300000000000000000000000000000000000000-22−2i2i0000000000001-1i3−i300i−i−330000000000
χ8666-6-600-36i−6i-33i3−3i33i3−3i3330−3i3i−3333000000000000000000000000000000000000002-22i−2i000000000000-11i3−i300−ii−330000000000
χ8766-6-600-36i−6i-33i3−3i33i3−3i3330−3i3i−333300000000000000000000000000000000000000-22−2i2i0000000000001-1−i3i300i−i3−30000000000
χ8866-6-600-3−6i6i-3−3i33i3−3i33i33303i−3i−3333000000000000000000000000000000000000002-2−2i2i000000000000-11−i3i300i−i−330000000000
χ8966-6-600-3−6i6i-3−3i33i3−3i33i33303i−3i−333300000000000000000000000000000000000000-222i−2i0000000000001-1i3−i300−ii3−30000000000
χ9066-6-600-3−6i6i-33i3−3i33i3−3i33303i−3i33−33000000000000000000000000000000000000002-2−2i2i000000000000-11i3−i300i−i3−30000000000
χ9166-6-600-3−6i6i-33i3−3i33i3−3i33303i−3i33−3300000000000000000000000000000000000000-222i−2i0000000000001-1−i3i300−ii−330000000000
χ9212-1212-1212-12-6006-6-6666-60000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-1212-600666-6-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121200-6006−6i36i36i3−6i3-660000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-121200-60066i3−6i3−6i36i3-660000000000000000000000000000000000000000000000000000000000000000000000000000000

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