Finite Group Databasebeta

← Group #13150683

Character table — Group #13150683

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order122222344666666641212121233666666121212123666666666661212121212121212121212121212224444442244444466661212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-11-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-111-1-11111-1-1-1-111-1-1-111-1
χ61111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-11
χ71111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11-11-11-1-1111111-1-1-1-1-1-1111-1-11
χ81111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1111-1-1-111-1-1-1-11111-1-111-111-1
χ91111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1111-1-111-1-111-1-1-1-111-11-11
χ101111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1111-111-111-1-1-1-111-1-111-1-1111-11-1
χ111111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-11111-1-111-1-111-1-11-11-1
χ121111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-111-111-1-111-1-111-1-11111-1-1-11-11
χ131111-1-11-1-11-1-1-1-1111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-111-1-11-11-1111111-1-1-1-111-1-1-1-111-1-1
χ141111-1-11-1-11-1-1-1-1111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1111-111-1-1-111111-1-11111-1-1-1-1-1-1-1-111
χ151111-1-11-1-11-1-1-1-1111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-1-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-111
χ161111-1-11-1-11-1-1-1-1111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ172222222222222222222222-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12200220020000200-1-1-1-100000000-1-1-1-10000
χ182222222222222222222222-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-200-2-200-20000-20011110000000011110000
χ19222222222222222222222-1222-1-1-122222-1-1-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000022020020000000000000000-1-1-1-1
χ20222222222222222222222-1222-1-1-122222-1-1-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000-2-20-200-200000000000000001111
χ212222222-2-22222222-2-2-2-2-22-1-1-1222-11111-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111122002200-20000-200-1-11100000000-1-1110000
χ222222222-2-22222222-2-2-2-2-22-1-1-1222-11111-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111111-2-200-2-2002000020011-1-10000000011-1-10000
χ232222222-2-22222222-2-2-2-2-2-1222-1-1-12-2-2-2-2-1-1-122-1-1-1-1-1-1-11111-2-2111111110000000002-20-20020000000000000000-111-1
χ242222222-2-22222222-2-2-2-2-2-1222-1-1-12-2-2-2-2-1-1-122-1-1-1-1-1-1-11111-2-211111111000000000-220200-200000000000000001-1-11
χ252222-2-22222-2-2-2-222-222-2-22-1-1-1222-1-1-1-1-1-1-2-211-1-11111-122-2-211-1-1-1-111112200-2-200-20000200-1-1110000000011-1-10000
χ262222-2-22222-2-2-2-222-222-2-22-1-1-1222-1-1-1-1-1-1-2-211-1-11111-122-2-211-1-1-1-11111-2-200220020000-20011-1-100000000-1-1110000
χ272222-2-22222-2-2-2-222-222-2-2-1222-1-1-122222-111-2-2-1-11111-1-1-111-2-2-1-1-1-11111000000000220-200-20000000000000000-11-11
χ282222-2-22222-2-2-2-222-222-2-2-1222-1-1-122222-111-2-2-1-11111-1-1-111-2-2-1-1-1-11111000000000-2-20200200000000000000001-11-1
χ292222-2-22-2-22-2-2-2-2222-2-2222-1-1-1222-11111-1-2-211-1-11111-1-2-222-1-11111-1-1-1-12200-2-20020000-200-1-1-1-10000000011110000
χ302222-2-22-2-22-2-2-2-2222-2-2222-1-1-1222-11111-1-2-211-1-11111-1-2-222-1-11111-1-1-1-1-2-2002200-20000200111100000000-1-1-1-10000
χ312222-2-22-2-22-2-2-2-2222-2-222-1222-1-1-12-2-2-2-2-111-2-2-1-11111-111-1-1221111-1-1-1-10000000002-20200-20000000000000000-1-111
χ322222-2-22-2-22-2-2-2-2222-2-222-1222-1-1-12-2-2-2-2-111-2-2-1-11111-111-1-1221111-1-1-1-1000000000-220-2002000000000000000011-1-1
χ332-22-20022i−2i-200002-202i−2i00222-22-2-2-22i2i−2i−2i200002-20000-22i−2i00002i2i−2i−2i0000002-2002i−2i0000000000002-2002i−2i0000000000
χ342-22-20022i−2i-200002-202i−2i00222-22-2-2-22i2i−2i−2i200002-20000-22i−2i00002i2i−2i−2i000000-2200−2i2i000000000000-2200−2i2i0000000000
χ352-22-2002−2i2i-200002-20−2i2i00222-22-2-2-2−2i−2i2i2i200002-20000-2−2i2i0000−2i−2i2i2i0000002-200−2i2i0000000000002-200−2i2i0000000000
χ362-22-2002−2i2i-200002-20−2i2i00222-22-2-2-2−2i−2i2i2i200002-20000-2−2i2i0000−2i−2i2i2i000000-22002i−2i000000000000-22002i−2i0000000000
χ372-2-222-2200-222-2-2-220000022-2-2-2-222000022-22-2-2-222-2-22000000000000002-2002-200000000002-200000000002-2000000
χ382-2-222-2200-222-2-2-220000022-2-2-2-222000022-22-2-2-222-2-2200000000000000-2200-220000000000-220000000000-22000000
χ392-2-222-2200-222-2-2-22000002-111-2-22-1−i3i3−i3i3-12-2-1111-1-111-10000−i3i3−i3i3−i3i3−i3−i3i3i32-2002-20000000000-11−i3i300000000-11−i3i30000
χ402-2-222-2200-222-2-2-22000002-111-2-22-1−i3i3−i3i3-12-2-1111-1-111-10000−i3i3−i3i3−i3i3−i3−i3i3i3-2200-2200000000001-1i3−i3000000001-1i3−i30000
χ412-2-222-2200-222-2-2-22000002-111-2-22-1i3−i3i3−i3-12-2-1111-1-111-10000i3−i3i3−i3i3−i3i3i3−i3−i32-2002-20000000000-11i3−i300000000-11i3−i30000
χ422-2-222-2200-222-2-2-22000002-111-2-22-1i3−i3i3−i3-12-2-1111-1-111-10000i3−i3i3−i3i3−i3i3i3−i3−i3-2200-2200000000001-1−i3i3000000001-1−i3i30000
χ432-2-22-22200-2-2-222-220000022-2-2-2-22200002-22-22-2-2-2-2222000000000000002-200-2200000000002-20000000000-22000000
χ442-2-22-22200-2-2-222-220000022-2-2-2-22200002-22-22-2-2-2-222200000000000000-22002-20000000000-2200000000002-2000000
χ452-2-22-22200-2-2-222-22000002-111-2-22-1−i3i3−i3i3-1-221-11111-1-1-10000i3−i3−i3i3−i3i3i3i3−i3−i32-200-220000000000-11i3−i3000000001-1−i3i30000
χ462-2-22-22200-2-2-222-22000002-111-2-22-1−i3i3−i3i3-1-221-11111-1-1-10000i3−i3−i3i3−i3i3i3i3−i3−i3-22002-200000000001-1−i3i300000000-11i3−i30000
χ472-2-22-22200-2-2-222-22000002-111-2-22-1i3−i3i3−i3-1-221-11111-1-1-10000−i3i3i3−i3i3−i3−i3−i3i3i32-200-220000000000-11−i3i3000000001-1i3−i30000
χ482-2-22-22200-2-2-222-22000002-111-2-22-1i3−i3i3−i3-1-221-11111-1-1-10000−i3i3i3−i3i3−i3−i3−i3i3i3-22002-200000000001-1i3−i300000000-11−i3i30000
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
χ514444-4-44444-4-4-4-444-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000000000
χ524444-4-44-4-44-4-4-4-4444-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000000000
χ5344-4-40040040000-4-40000044-44-44-4-4000040000-440000-400000000000000000000000000000000000000000000000000
χ5444-4-40040040000-4-4000004-22-2-44-4223−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000000000
χ5544-4-40040040000-4-4000004-22-2-44-42−232323−23-200002-200002000000−232323−230000000000000000000000000000000000000000
χ5644-4-40040040000-4-400000-24-442-22-40000-200002-2000020023−2300000023−2323−23000000000000000000000000000000000000
χ5744-4-40040040000-4-400000-24-442-22-40000-200002-20000200−2323000000−2323−2323000000000000000000000000000000000000
χ5844-4-40040040000-4-400000-2-22-22-22223−23−232310000-113-33-3-10023−2300−333−3−33−33000000000000000000000000000000000000
χ5944-4-40040040000-4-400000-2-22-22-22223−23−232310000-11-33-33-100−232300−333−33−33−3000000000000000000000000000000000000
χ6044-4-40040040000-4-400000-2-22-22-222−232323−2310000-113-33-3-100−2323003−3−333−33−3000000000000000000000000000000000000
χ6144-4-40040040000-4-400000-2-22-22-222−232323−2310000-11-33-33-10023−23003−3−33−33−33000000000000000000000000000000000000
χ624-44-40044i−4i-400004-404i−4i004-2-224-4-42−2i−2i2i2i-20000-22000024i−4i0000−2i−2i2i2i0000000000000000000000000000000000000000
χ634-44-40044i−4i-400004-404i−4i00-244-4-222-44i4i−4i−4i-20000-2200002−2i2i0000−2i−2i2i2i0000000000000000000000000000000000000000
χ644-44-40044i−4i-400004-404i−4i00-2-2-22-2222−2i−2i2i2i100001-13-3-33-1−2i2i0000ii−i−i−3i3i3i−3i000000000000000000000000000000000000
χ654-44-40044i−4i-400004-404i−4i00-2-2-22-2222−2i−2i2i2i100001-1-333-3-1−2i2i0000ii−i−i3i−3i−3i3i000000000000000000000000000000000000
χ664-44-4004−4i4i-400004-40−4i4i004-2-224-4-422i2i−2i−2i-20000-2200002−4i4i00002i2i−2i−2i0000000000000000000000000000000000000000
χ674-44-4004−4i4i-400004-40−4i4i00-244-4-222-4−4i−4i4i4i-20000-22000022i−2i00002i2i−2i−2i0000000000000000000000000000000000000000
χ684-44-4004−4i4i-400004-40−4i4i00-2-2-22-22222i2i−2i−2i100001-13-3-33-12i−2i0000−i−iii3i−3i−3i3i000000000000000000000000000000000000
χ694-44-4004−4i4i-400004-40−4i4i00-2-2-22-22222i2i−2i−2i100001-1-333-3-12i−2i0000−i−iii−3i3i3i−3i000000000000000000000000000000000000
χ704-4-444-4400-444-4-4-4400000-24-4-422-240000-2-224-422-2-222-200000000000000000000000000000000000000000000000000
χ714-4-444-4400-444-4-4-4400000-2-22222-2-2−2i32i3−2i32i31-22-22-1-111-1-110000−2i32i3i3−i3i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ724-4-444-4400-444-4-4-4400000-2-22222-2-22i3−2i32i3−2i31-22-22-1-111-1-1100002i3−2i3−i3i3−i3i3−i3−i3i3i3000000000000000000000000000000000000
χ734-4-44-44400-4-4-444-4400000-24-4-422-240000-22-2-442222-2-2-200000000000000000000000000000000000000000000000000
χ744-4-44-44400-4-4-444-4400000-2-22222-2-2−2i32i3−2i32i312-22-2-1-1-1-111100002i3−2i3i3−i3i3−i3−i3−i3i3i3000000000000000000000000000000000000
χ754-4-44-44400-4-4-444-4400000-2-22222-2-22i3−2i32i3−2i312-22-2-1-1-1-11110000−2i32i3−i3i3−i3i3i3i3−i3−i3000000000000000000000000000000000000
χ76666666-366-3-3-3-3-3-3-36-3-3-3-30000000000000000000000000000000000000000220022000200200000-1-1-1-1-1-1-1-100000000
χ77666666-366-3-3-3-3-3-3-36-3-3-3-30000000000000000000000000000000000000000-2-200-2-2000-200-2000001111111100000000
χ78666666-3-6-6-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000002200-2-2000200-200000-1-1-1-1111100000000
χ79666666-3-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000-2-20022000-2002000001111-1-1-1-100000000
χ806666-6-6-366-33333-3-3-6-3-3330000000000000000000000000000000000000000220022000-200-200000-1-111-1-11100000000
χ816666-6-6-366-33333-3-3-6-3-3330000000000000000000000000000000000000000-2-200-2-200020020000011-1-111-1-100000000
χ826666-6-6-3-6-6-33333-3-3633-3-300000000000000000000000000000000000000002200-2-2000-200200000-1-11111-1-100000000
χ836666-6-6-3-6-6-33333-3-3633-3-30000000000000000000000000000000000000000-2-20022000200-20000011-1-1-1-11100000000
χ846-66-600-36i−6i3−3i33i3−3i33i3-330−3i3i33−3300000000000000000000000000000000000000002-2002i−2i000000000000-11−i3i3−ii3−300000000
χ856-66-600-36i−6i3−3i33i3−3i33i3-330−3i3i33−330000000000000000000000000000000000000000-2200−2i2i0000000000001-1i3−i3i−i−3300000000
χ866-66-600-36i−6i33i3−3i33i3−3i3-330−3i3i−333300000000000000000000000000000000000000002-2002i−2i000000000000-11i3−i3−ii−3300000000
χ876-66-600-36i−6i33i3−3i33i3−3i3-330−3i3i−33330000000000000000000000000000000000000000-2200−2i2i0000000000001-1−i3i3i−i3−300000000
χ886-66-600-3−6i6i3−3i33i3−3i33i3-3303i−3i−333300000000000000000000000000000000000000002-200−2i2i000000000000-11−i3i3i−i−3300000000
χ896-66-600-3−6i6i3−3i33i3−3i33i3-3303i−3i−33330000000000000000000000000000000000000000-22002i−2i0000000000001-1i3−i3−ii3−300000000
χ906-66-600-3−6i6i33i3−3i33i3−3i3-3303i−3i33−3300000000000000000000000000000000000000002-200−2i2i000000000000-11i3−i3i−i3−300000000
χ916-66-600-3−6i6i33i3−3i33i3−3i3-3303i−3i33−330000000000000000000000000000000000000000-22002i−2i0000000000001-1−i3i3−ii−3300000000
χ921212-12-1200-600-6−6i36i36i3−6i3660000000000000000000000000000000000000000000000000000000000000000000000000000000
χ931212-12-1200-600-66i3−6i3−6i36i3660000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121212-12-6006-6-6666-60000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-1212-600666-6-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000

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