Finite Group Databasebeta

← Group #13137916

Character table — Group #13137916

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order1222344666121233666666412123666121212122212121212121212121212444446688881212242424242424242426612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111-1-11111111111-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111
χ511111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1
χ811111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111-1-111
χ92222222222222-1-122-1-12222-1-1-1-12-1-122222-1-1-1-1-1-1-1-120000-1-10000-1-1000000002-1-10000
χ102222222222222-1-122-1-12222-1-1-1-12-1-12-2-222-1-1-1-1-1-1-1-1-200001100001100000000-2110000
χ112222222222222-1-122-1-12-2-2-2-1-1-1-12-1-1222-2-211-1-1111120000-1-10000-1-100000000-2110000
χ122222222222222-1-122-1-12-2-2-2-1-1-1-12-1-12-2-2-2-211-1-11111-2000011000011000000002-1-10000
χ13222222222222-122-1-122-1222-1-1-1-1-122-100-1-122-1-1-1-1-1-100022000022000000-1-1-1-100000-1-1
χ14222222222222-122-1-122-1222-1-1-1-1-122-100-1-122-1-1-1-1-1-1000-2-20000-2-200000011110000011
χ15222222222222-122-1-122-1-2-2-2-1-1-1-1-122-10011-2-2-1-11111000220000-2-2000000111100000-1-1
χ16222222222222-122-1-122-1-2-2-2-1-1-1-1-122-10011-2-2-1-11111000-2-2000022000000-1-1-1-10000011
χ1722222-2-2222-2-2222222220002222-2-2-2-2220000-2-20000-20000220000-2-2000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-20000-2-2000020000-2-2000022000000000000000
χ1922222-2-2222-2-22-1-122-1-12000-1-1-1-1-211-22200−i3i311−i3−i3i3i3-20000-1-1000011000000000−i3i30000
χ2022222-2-2222-2-22-1-122-1-12000-1-1-1-1-211-22200i3−i311i3i3−i3−i3-20000-1-1000011000000000i3−i30000
χ2122222-2-2222-2-22-1-122-1-12000-1-1-1-1-211-2-2-200−i3i311−i3−i3i3i320000110000-1-1000000000i3−i30000
χ2222222-2-2222-2-22-1-122-1-12000-1-1-1-1-211-2-2-200i3−i311i3i3−i3−i320000110000-1-1000000000−i3i30000
χ2322-2-2200-22-20022-2-222-2-20002-2-2200002-20000000000000002-2−i2i2−i2i200−i2−i2i2i2−i2−i2i2i20000000
χ2422-2-2200-22-20022-2-222-2-20002-2-2200002-20000000000000002-2i2−i2i2−i200i2i2−i2−i2i2i2−i2−i20000000
χ2522-2-2200-22-20022-2-222-2-20002-2-220000-22000000000000000-22−i2i2i2−i200−i2−i2i2i2i2i2−i2−i20000000
χ2622-2-2200-22-20022-2-222-2-20002-2-220000-22000000000000000-22i2−i2−i2i200i2i2−i2−i2−i2−i2i2i20000000
χ272-22-222-22-2-22-222-22-2-22-20002-22-2-22-220000002-200000002i−2i0000000000000000000002i−2i
χ282-22-222-22-2-22-222-22-2-22-20002-22-2-22-220000002-20000000−2i2i000000000000000000000−2i2i
χ292-22-222-22-2-22-2-12-2-11-221000-11-1112-2-1003−300-113−33−30002i−2i000000000000−i3i3−i3i300000−ii
χ302-22-222-22-2-22-2-12-2-11-221000-11-1112-2-1003−300-113−33−3000−2i2i000000000000i3−i3i3−i300000i−i
χ312-22-222-22-2-22-2-12-2-11-221000-11-1112-2-100−3300-11−33−330002i−2i000000000000i3−i3i3−i300000−ii
χ322-22-222-22-2-22-2-12-2-11-221000-11-1112-2-100−3300-11−33−33000−2i2i000000000000−i3i3−i3i300000i−i
χ332-22-22-222-2-2-2222-22-2-22-20002-22-22-22-2000000-22000002i−2i0000000000000000000002i−2i00
χ342-22-22-222-2-2-2222-22-2-22-20002-22-22-22-2000000-2200000−2i2i000000000000000000000−2i2i00
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
χ3744444-4-4444-4-4-244-2-244-2000-2-2-2-22-4-420000002200000000000000000000000000000000
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
χ4044-4-4400-44-4004-22-44-22-4000-222-200004-4000000000000000-22000000000000000000000
χ4144-4-4400-44-4004-22-44-22-4000-222-20000-440000000000000002-2000000000000000000000
χ4244-4-4400-44-400-24-42-24-42000-222-20000000000000000000000000−2i22i2000000i2i2−i2−i20000000
χ4344-4-4400-44-400-24-42-24-42000-222-200000000000000000000000002i2−2i2000000−i2−i2i2i20000000
χ444-44-444-44-4-44-44-224-42-2-4000-22-22-4-224000000-2200000000000000000000000000000000
χ454-44-444-44-4-44-4-2-22-222-220001-11-12-22-20023−23001-1−33−330000000000000000000000000000
χ464-44-444-44-4-44-4-2-22-222-220001-11-12-22-200−2323001-13−33−30000000000000000000000000000
χ474-44-44-444-4-4-444-224-42-2-4000-22-2242-2-40000002-200000000000000000000000000000000
χ484-44-44-444-4-4-44-24-4-22-442000-22-22-2-4420000002-200000000000000000000000000000000
χ494-44-44-444-4-4-44-2-22-222-220001-11-1-22-22000000-113i−3i−3i3i0000000000000000000000000000
χ504-44-44-444-4-4-44-2-22-222-220001-11-1-22-22000000-11−3i3i3i−3i0000000000000000000000000000
χ514-4-44400-4-4400444-4-4-4-4400044-4-400000000000000000000000000000000000000000000
χ524-4-44400-4-44004-2-2-4-4224000-2-22200000000000000000000000000023−23000000000000000
χ534-4-44400-4-44004-2-2-4-4224000-2-222000000000000000000000000000−2323000000000000000
χ544-4-44400-4-4400-24422-4-4-2000-2-2220000000000000000000000000000000006−6−660000000
χ554-4-44400-4-4400-24422-4-4-2000-2-222000000000000000000000000000000000−666−60000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000000220000220000-1-1-1-10000000-1-100
χ576666-366-3-3-3-3-3000000006-3-3000000000000000000000-2-20000-2-20000111100000001100
χ586666-366-3-3-3-3-300000000-633000000000000000000000220000-2-2000011110000000-1-100
χ596666-366-3-3-3-3-300000000-633000000000000000000000-2-20000220000-1-1-1-100000001100
χ606-66-6-3-66-3333-300000000033−330000000000000000000002i−2i0000000000−i3i3−i3i30000000−ii00
χ616-66-6-3-66-3333-300000000033−33000000000000000000000−2i2i0000000000i3−i3i3−i30000000i−i00
χ626-66-6-3-66-3333-3000000000−33330000000000000000000002i−2i0000000000i3−i3i3−i30000000−ii00
χ636-66-6-3-66-3333-3000000000−3333000000000000000000000−2i2i0000000000−i3i3−i3i30000000i−i00
χ6488-8-8800-88-800-4-444-4-4440002-2-2200000000000000000000000000000000000000000000
χ658-8-88800-8-8800-4-4-44444-400022-2-200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-6006-660000000000000000000000000000000000000000−2i22i20000i2i2−i2−i200000000000
χ681212-12-12-6006-6600000000000000000000000000000000000000002i2−2i20000−i2−i2i2i200000000000
χ6912-1212-12-612-12-666-6600000000000000000000000000000000000000000000000000000000000
χ7012-12-1212-60066-600000000000000000000000000000000000000000000006−6−6600000000000
χ7112-12-1212-60066-60000000000000000000000000000000000000000000000−666−600000000000

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