Finite Group Databasebeta

← Group #13140981

Character table — Group #13140981

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order12223446661212336666664121236661212121244121212121212121212124444488881212121224242424242424244121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111
χ31111111111111111111111111111111-1-11111111111-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1
χ511111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11-1-11111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-111
χ92222222222222-122-1-12-1222-1-1-1-12-1-122222-1-1-1-1-1-1-1-1200000000-1-1-1-10000000020000-1-1
χ102222222222222-122-1-12-1222-1-1-1-12-1-12-2-222-1-1-1-1-1-1-1-1-200000000111100000000-2000011
χ112222222222222-122-1-12-1-2-2-2-1-1-1-12-1-1222-2-211-1-11111200000000-1-1-1-100000000-2000011
χ122222222222222-122-1-12-1-2-2-2-1-1-1-12-1-12-2-2-2-211-1-11111-20000000011110000000020000-1-1
χ13222222222222-12-1-122-12222-1-1-1-1-122-100-1-122-1-1-1-1-1-102200220000000000-1-1-1-1000-1-100
χ14222222222222-12-1-122-12222-1-1-1-1-122-100-1-122-1-1-1-1-1-10-2-200-2-2000000000011110001100
χ15222222222222-12-1-122-12-2-2-2-1-1-1-1-122-10011-2-2-1-1111102200-2-200000000001111000-1-100
χ16222222222222-12-1-122-12-2-2-2-1-1-1-1-122-10011-2-2-1-111110-2-200220000000000-1-1-1-10001100
χ1722222-2-2222-2-2222222220002222-2-2-2-2220000-2-20000-20000000022-2-2000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-20000-2-20000200000000-2-222000000000000000
χ1922222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-22200−i3i311−i3−i3i3i3-200000000-1-1110000000000000−i3i3
χ2022222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-22200i3−i311i3i3−i3−i3-200000000-1-1110000000000000i3−i3
χ2122222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-2-2-200−i3i311−i3−i3i3i320000000011-1-10000000000000i3−i3
χ2222222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-2-2-200i3−i311i3i3−i3−i320000000011-1-10000000000000−i3i3
χ2322-2-22002-2-200222-22-2-2-200022-2-200002-20000000000000002−22−22-20022−2−222−2−20000000
χ2422-2-22002-2-200222-22-2-2-200022-2-200002-2000000000000000−22−222-200−2−222−2−2220000000
χ2522-2-22002-2-200222-22-2-2-200022-2-20000-220000000000000002−2−22-2200−2−22222−2−20000000
χ2622-2-22002-2-200222-22-2-2-200022-2-20000-22000000000000000−222−2-220022−2−2−2−2220000000
χ272-2-2222-2-2-222-222-22-2-2-220002-2-2222-2-20000002-2000002i−2i0000000000000000000002i−2i00
χ282-2-2222-2-2-222-222-22-2-2-220002-2-2222-2-20000002-200000−2i2i000000000000000000000−2i2i00
χ292-2-2222-2-2-222-2-121-1-2-212000-111-1-12-2100−i3i300-11−i3i3−i3i302i−2i000000000000003−33−3000−ii00
χ302-2-2222-2-2-222-2-121-1-2-212000-111-1-12-2100−i3i300-11−i3i3−i3i30−2i2i00000000000000−33−33000i−i00
χ312-2-2222-2-2-222-2-121-1-2-212000-111-1-12-2100i3−i300-11i3−i3i3−i302i−2i00000000000000−33−33000−ii00
χ322-2-2222-2-2-222-2-121-1-2-212000-111-1-12-2100i3−i300-11i3−i3i3−i30−2i2i000000000000003−33−3000i−i00
χ332-2-222-22-2-22-2222-22-2-2-220002-2-22-2-222000000-2200000002-2000000000000000002-20000
χ342-2-222-22-2-22-2222-22-2-2-220002-2-22-2-222000000-220000000-2200000000000000000-220000
χ35444444444444-2-2-2-2-2-2-2-24441111-2-2-2-200-2-2-2-21111110000000000000000000000000000
χ36444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-200222211-1-1-1-10000000000000000000000000000
χ3744444-4-4444-4-4-24-2-244-24000-2-2-2-22-4-420000002200000000000000000000000000000000
χ3844444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000−2i32i3-1-1i3i3−i3−i30000000000000000000000000000
χ3944444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200002i3−2i3-1-1−i3−i3i3i30000000000000000000000000000
χ4044-4-44004-4-4004-24-4-22-42000-2-22200004-40000000000000000000-2200000000000000000
χ4144-4-44004-4-4004-24-4-22-42000-2-2220000-4400000000000000000002-200000000000000000
χ4244-4-44004-4-400-24-224-42-4000-2-22200000000000000000000022−220000000000−2−2220000000
χ4344-4-44004-4-400-24-224-42-4000-2-222000000000000000000000−2222000000000022−2−20000000
χ444-44-4400-44-40044-4-4-444-40004-44-400000000000000000000000000000000000000000000
χ454-44-4400-44-4004-2-4-42-242000-22-22000000000000000000000000000−2i32i3000000000000000
χ464-44-4400-44-4004-2-4-42-242000-22-220000000000000000000000000002i3−2i3000000000000000
χ474-44-4400-44-400-2422-44-2-4000-22-220000000000000000000000000000000006−6−660000000
χ484-44-4400-44-400-2422-44-2-4000-22-22000000000000000000000000000000000−666−60000000
χ494-4-4444-4-4-444-44-2-4422-4-2000-222-24-22-4000000-2200000000000000000000000000000000
χ504-4-4444-4-4-444-4-2-22-2222-20001-1-11-2-22200−2i32i3001-1i3−i3i3−i30000000000000000000000000000
χ514-4-4444-4-4-444-4-2-22-2222-20001-1-11-2-222002i3−2i3001-1−i3i3−i3i30000000000000000000000000000
χ524-4-444-44-4-44-444-2-4422-4-2000-222-2-42-240000002-200000000000000000000000000000000
χ534-4-444-44-4-44-44-242-2-4-424000-222-22-44-20000002-200000000000000000000000000000000
χ544-4-444-44-4-44-44-2-22-2222-20001-1-1122-2-2000000-113-3-330000000000000000000000000000
χ554-4-444-44-4-44-44-2-22-2222-20001-1-1122-2-2000000-11-333-30000000000000000000000000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000000002200220000-1-1-1-100000-1-10000
χ576666-366-3-3-3-3-3000000006-3-300000000000000000000000-2-200-2-20000111100000110000
χ586666-366-3-3-3-3-300000000-633000000000000000000000002200-2-20000111100000-1-10000
χ596666-366-3-3-3-3-300000000-63300000000000000000000000-2-200220000-1-1-1-100000110000
χ606-6-66-3-6633-33-3000000000−3i33i3000000000000000000000002-200000000−i3i3−i3i300000-110000
χ616-6-66-3-6633-33-3000000000−3i33i300000000000000000000000-2200000000i3−i3i3−i3000001-10000
χ626-6-66-3-6633-33-30000000003i3−3i3000000000000000000000002-200000000i3−i3i3−i300000-110000
χ636-6-66-3-6633-33-30000000003i3−3i300000000000000000000000-2200000000−i3i3−i3i3000001-10000
χ6488-8-88008-8-800-4-4-44-444400022-2-200000000000000000000000000000000000000000000
χ658-88-8800-88-800-4-4444-4-440002-22-200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-600-666000000000000000000000000000000000000000022−220000−2−22200000000000
χ681212-12-12-600-6660000000000000000000000000000000000000000−2222000022−2−200000000000
χ6912-1212-12-6006-660000000000000000000000000000000000000000000000i6−i6−i6i600000000000
χ7012-1212-12-6006-660000000000000000000000000000000000000000000000−i6i6i6−i600000000000
χ7112-12-1212-612-1266-6-6600000000000000000000000000000000000000000000000000000000000

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