Finite Group Databasebeta

← Group #13140997

Character table — Group #13140997

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order12223446661212336666664121236661212121222121212121212121212122222466888812122424242424242424466661212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111
χ31111111111111111111111111111111-1-1111111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111-1-11111111111-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-111-1-1
χ511111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-11-1-11111
χ92222222222222-12-1-1-122222-1-1-1-1-122-100-1-122-1-1-1-1-1-100220000022000000-1-1-1-1000-1-100
χ102222222222222-12-1-1-122222-1-1-1-1-122-100-1-122-1-1-1-1-1-100-2-200000-2-200000011110001100
χ112222222222222-12-1-1-122-2-2-2-1-1-1-1-122-10011-2-2-1-11111002200000-2-20000001111000-1-100
χ122222222222222-12-1-1-122-2-2-2-1-1-1-1-122-10011-2-2-1-1111100-2-20000022000000-1-1-1-10001100
χ13222222222222-12-1222-1-1222-1-1-1-12-1-122222-1-1-1-1-1-1-1-100002-1-10000-1-10000000020000-1-1
χ14222222222222-12-1222-1-1222-1-1-1-12-1-12-2-222-1-1-1-1-1-1-1-10000-21100001100000000-2000011
χ15222222222222-12-1222-1-1-2-2-2-1-1-1-12-1-1222-2-211-1-1111100002-1-10000-1-100000000-2000011
χ16222222222222-12-1222-1-1-2-2-2-1-1-1-12-1-12-2-2-2-211-1-111110000-2110000110000000020000-1-1
χ1722222-2-2222-2-2222222220002222-2-2-2-2220000-2-200000000-2220000-2-2000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-20000-2-2000000002-2-2000022000000000000000
χ1922222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-22200−i3i311−i3−i3i3i30000-2-1-10000110000000000000−i3i3
χ2022222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-22200i3−i311i3i3−i3−i30000-2-1-10000110000000000000i3−i3
χ2122222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-2-2-200−i3i311−i3−i3i3i300002110000-1-10000000000000i3−i3
χ2222222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-2-2-200i3−i311i3i3−i3−i300002110000-1-10000000000000−i3i3
χ2322-2-22002-2-2002222-2-2-2-200022-2-200002-20000000000000002-2−i2i2−i2i200−i2−i2i2i2−i2−i2i2i20000000
χ2422-2-22002-2-2002222-2-2-2-200022-2-200002-20000000000000002-2i2−i2i2−i200i2i2−i2−i2i2i2−i2−i20000000
χ2522-2-22002-2-2002222-2-2-2-200022-2-20000-22000000000000000-22−i2i2i2−i200−i2−i2i2i2i2i2−i2−i20000000
χ2622-2-22002-2-2002222-2-2-2-200022-2-20000-22000000000000000-22i2−i2−i2i200i2i2−i2−i2−i2−i2i2i20000000
χ272-22-222-2-2-222-222-2-2-222-20002-2-22-22-220000002-20000002-2000000000000000000002-200
χ282-22-222-2-2-222-222-2-2-222-20002-2-22-22-220000002-2000000-2200000000000000000000-2200
χ292-22-222-2-2-222-22-1-211-12-2000-111-112-2-100−i3i300-11−i3i3−i3i3002-20000000000000−i3i3−i3i3000-1100
χ302-22-222-2-2-222-22-1-211-12-2000-111-112-2-100−i3i300-11−i3i3−i3i300-220000000000000i3−i3i3−i30001-100
χ312-22-222-2-2-222-22-1-211-12-2000-111-112-2-100i3−i300-11i3−i3i3−i3002-20000000000000i3−i3i3−i3000-1100
χ322-22-222-2-2-222-22-1-211-12-2000-111-112-2-100i3−i300-11i3−i3i3−i300-220000000000000−i3i3−i3i30001-100
χ332-22-22-22-2-22-2222-2-2-222-20002-2-222-22-2000000-2200002-2000000000000000000002-20000
χ342-22-22-22-2-22-2222-2-2-222-20002-2-222-22-2000000-220000-2200000000000000000000-220000
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
χ3744444-4-4444-4-44-24-2-2-244000-2-2-2-22-4-420000002200000000000000000000000000000000
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
χ4044-4-44004-4-4004-24-222-4-4000-2-2220000000000000000000000000−2i22i2000000i2i2−i2−i20000000
χ4144-4-44004-4-4004-24-222-4-4000-2-22200000000000000000000000002i2−2i2000000−i2−i2i2i20000000
χ4244-4-44004-4-400-24-24-4-422000-2-22200004-4000000000000000-22000000000000000000000
χ4344-4-44004-4-400-24-24-4-422000-2-2220000-440000000000000002-2000000000000000000000
χ444-44-444-4-4-444-4-242-4-44-22000-222-2-4-224000000-2200000000000000000000000000000000
χ454-44-444-4-4-444-4-2-2222-2-220001-1-112-22-200−2i32i3001-1i3−i3i3−i30000000000000000000000000000
χ464-44-444-4-4-444-4-2-2222-2-220001-1-112-22-2002i3−2i3001-1−i3i3−i3i30000000000000000000000000000
χ474-44-44-44-4-44-444-2-422-24-4000-222-2-2-4420000002-200000000000000000000000000000000
χ484-44-44-44-4-44-44-242-4-44-22000-222-242-2-40000002-200000000000000000000000000000000
χ494-44-44-44-4-44-44-2-2222-2-220001-1-11-22-22000000-113-3-330000000000000000000000000000
χ504-44-44-44-4-44-44-2-2222-2-220001-1-11-22-22000000-11-333-30000000000000000000000000000
χ514-4-44400-44-40044-4-44-4-440004-44-400000000000000000000000000000000000000000000
χ524-4-44400-44-4004-2-42-22-44000-22-220000000000000000000000000000000006−6−660000000
χ534-4-44400-44-4004-2-42-22-44000-22-22000000000000000000000000000000000−666−60000000
χ544-4-44400-44-400-242-44-42-2000-22-2200000000000000000000000000023−23000000000000000
χ554-4-44400-44-400-242-44-42-2000-22-22000000000000000000000000000−2323000000000000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000002200000220000-1-1-1-100000-1-10000
χ576666-366-3-3-3-3-3000000006-3-300000000000000000000-2-200000-2-20000111100000110000
χ586666-366-3-3-3-3-300000000-633000000000000000000002200000-2-20000111100000-1-10000
χ596666-366-3-3-3-3-300000000-63300000000000000000000-2-200000220000-1-1-1-100000110000
χ606-66-6-3-6633-33-3000000000−3i33i3000000000000000000002-200000000000−i3i3−i3i300000-110000
χ616-66-6-3-6633-33-3000000000−3i33i300000000000000000000-2200000000000i3−i3i3−i3000001-10000
χ626-66-6-3-6633-33-30000000003i3−3i3000000000000000000002-200000000000i3−i3i3−i300000-110000
χ636-66-6-3-6633-33-30000000003i3−3i300000000000000000000-2200000000000−i3i3−i3i3000001-10000
χ6488-8-88008-8-800-4-4-4-4444400022-2-200000000000000000000000000000000000000000000
χ658-8-88800-88-800-4-444-444-40002-22-200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-600-6660000000000000000000000000000000000000000−2i22i20000i2i2−i2−i200000000000
χ681212-12-12-600-66600000000000000000000000000000000000000002i2−2i20000−i2−i2i2i200000000000
χ6912-1212-12-612-1266-6-6600000000000000000000000000000000000000000000000000000000000
χ7012-12-1212-6006-6600000000000000000000000000000000000000000000006−6−6600000000000
χ7112-12-1212-6006-660000000000000000000000000000000000000000000000−666−600000000000

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