Finite Group Databasebeta

← Group #13140583

Character table — Group #13140583

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order12223446661212336666662663666121212124466666666121224444668888121224242424242424244121212121212
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
χ511111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1-1-11111-1-1-1-1111-1-111
χ92222222222222-12-12-12-1222-1-1-1-12-12-10022-1-1-1-1-1-1-1-100022000022000000-1-1-1-100000-1-1
χ102222222222222-12-12-12-1222-1-1-1-12-12-10022-1-1-1-1-1-1-1-1000-2-20000-2-200000011110000011
χ112222222222222-12-12-12-1-2-2-2-1-1-1-12-12-100-2-2111111-1-1000220000-2-2000000111100000-1-1
χ122222222222222-12-12-12-1-2-2-2-1-1-1-12-12-100-2-2111111-1-1000-2-2000022000000-1-1-1-10000011
χ13222222222222-12-12-12-12222-1-1-1-1-12-1200-1-122-1-1-1-1-1-10220000220000-1-1-1-10000000-1-100
χ14222222222222-12-12-12-12222-1-1-1-1-12-1200-1-122-1-1-1-1-1-10-2-20000-2-20000111100000001100
χ15222222222222-12-12-12-12-2-2-2-1-1-1-1-12-120011-2-21111-1-10220000-2-2000011110000000-1-100
χ16222222222222-12-12-12-12-2-2-2-1-1-1-1-12-120011-2-21111-1-10-2-20000220000-1-1-1-100000001100
χ1722222-2-2222-2-2222222220002222-2-2-2-22200000000-2-2-20000-2-2000022000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-200000000-2-220000220000-2-2000000000000000
χ1922-2-222-2-22-22-222-2-222-2-20002-2-222-2-2200000000002-202i−2i0000000000000000000002i−2i00
χ2022-2-222-2-22-22-222-2-222-2-20002-2-222-2-2200000000002-20−2i2i000000000000000000000−2i2i00
χ2122-2-222-2-22-22-2-121-2-121-2000-111-1-1-21200−i3i300−i3−i3i3i3-1102i−2i000000000033−3−30000000−ii00
χ2222-2-222-2-22-22-2-121-2-121-2000-111-1-1-21200−i3i300−i3−i3i3i3-110−2i2i0000000000−3−3330000000i−i00
χ2322-2-222-2-22-22-2-121-2-121-2000-111-1-1-21200i3−i300i3i3−i3−i3-1102i−2i0000000000−3−3330000000−ii00
χ2422-2-222-2-22-22-2-121-2-121-2000-111-1-1-21200i3−i300i3i3−i3−i3-110−2i2i000000000033−3−30000000i−i00
χ2522-2-22-22-22-2-2222-2-222-2-20002-2-22-222-20000000000-220002i−2i0000000000000000000002i−2i
χ2622-2-22-22-22-2-2222-2-222-2-20002-2-22-222-20000000000-22000−2i2i000000000000000000000−2i2i
χ2722-2-22-22-22-2-222-1-212-1-21000-111-1-2-1210000−i3i3−i3i3−i3i31-10002i−2i00000000000033−3−300000−ii
χ2822-2-22-22-22-2-222-1-212-1-21000-111-1-2-1210000−i3i3−i3i3−i3i31-1000−2i2i000000000000−3−33300000i−i
χ2922-2-22-22-22-2-222-1-212-1-21000-111-1-2-1210000i3−i3i3−i3i3−i31-10002i−2i000000000000−3−33300000−ii
χ3022-2-22-22-22-2-222-1-212-1-21000-111-1-2-1210000i3−i3i3−i3i3−i31-1000−2i2i00000000000033−3−300000i−i
χ312-22-22002-2-20022-22-2-22-200022-2-200002i−2i000000000000000002−2−i2i22i−2i2−22−2−i2i2−i2i20000000
χ322-22-22002-2-20022-22-2-22-200022-2-200002i−2i00000000000000000−22i2−i22i−2i−22−22i2−i2i2−i20000000
χ332-22-22002-2-20022-22-2-22-200022-2-20000−2i2i000000000000000002−2i2−i2−2i2i2−22−2i2−i2i2−i20000000
χ342-22-22002-2-20022-22-2-22-200022-2-20000−2i2i00000000000000000−22−i2i2−2i2i−22−22−i2i2−i2i20000000
χ35444444444444-2-2-2-2-2-2-2-24441111-2-2-2-200-2-2-2-21111110000000000000000000000000000
χ36444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-2002222-1-1-1-1110000000000000000000000000000
χ3744444-4-4444-4-44-24-24-24-2000-2-2-2-2-42-420000000000220000000000000000000000000000
χ3844444-4-4444-4-4-24-24-24-24000-2-2-2-22-42-40000000000220000000000000000000000000000
χ3944444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000003-3-33-1-10000000000000000000000000000
χ4044444-4-4444-4-4-2-2-2-2-2-2-2-200011112222000000-333-3-1-10000000000000000000000000000
χ4144-4-444-4-44-44-44-2-424-2-42000-222-242-4-20000000000-220000000000000000000000000000
χ4244-4-444-4-44-44-4-2-222-2-2220001-1-11-222-200−2i32i300i3i3−i3−i31-10000000000000000000000000000
χ4344-4-444-4-44-44-4-2-222-2-2220001-1-11-222-2002i3−2i300−i3−i3i3i31-10000000000000000000000000000
χ4444-4-44-44-44-4-44-242-4-242-4000-222-224-2-400000000002-20000000000000000000000000000
χ4544-4-44-44-44-4-44-2-222-2-2220001-1-112-2-220000−2i32i3i3−i3i3−i3-110000000000000000000000000000
χ4644-4-44-44-44-4-44-2-222-2-2220001-1-112-2-2200002i3−2i3−i3i3−i3i3-110000000000000000000000000000
χ474-44-44004-4-4004-2-4-2-4242000-2-2220000000000000000000000000−2i22i2000000i2−i2i2−i20000000
χ484-44-44004-4-4004-2-4-2-4242000-2-22200000000000000000000000002i2−2i2000000−i2i2−i2i20000000
χ494-44-44004-4-400-24242-4-2-4000-2-2220000000000000000000000022−220000−22−2200000000000
χ504-44-44004-4-400-24242-4-2-4000-2-22200000000000000000000000−222200002−22−200000000000
χ514-4-44400-4-4400444-4-4-4-440004-44-400000000000000000000000000000000000000000000
χ524-4-44400-4-44004-242-42-4-2000-22-22000000000000000000000000000000000i6−i6−i6i60000000
χ534-4-44400-4-44004-242-42-4-2000-22-22000000000000000000000000000000000−i6i6i6−i60000000
χ544-4-44400-4-4400-24-2-42-424000-22-22000000000000000000000000000006−6−6600000000000
χ554-4-44400-4-4400-24-2-42-424000-22-2200000000000000000000000000000−666−600000000000
χ566666-366-3-3-3-3-3000000006-3-30000000022000000000020000-1-10000-1-1000000002-1-10000
χ576666-366-3-3-3-3-3000000006-3-300000000-2-20000000000-200001100001100000000-2110000
χ586666-366-3-3-3-3-300000000-6330000000022000000000020000-1-10000-1-100000000-2110000
χ596666-366-3-3-3-3-300000000-63300000000-2-20000000000-2000011000011000000002-1-10000
χ606666-3-6-6-3-3-333000000000−3i33i300000000220000000000-20000110000-1-1000000000−i3i30000
χ616666-3-6-6-3-3-333000000000−3i33i300000000-2-2000000000020000-1-1000011000000000i3−i30000
χ626666-3-6-6-3-3-3330000000003i3−3i300000000220000000000-20000110000-1-1000000000i3−i30000
χ636666-3-6-6-3-3-3330000000003i3−3i300000000-2-2000000000020000-1-1000011000000000−i3i30000
χ648-88-88008-8-800-4-44-444-4400022-2-200000000000000000000000000000000000000000000
χ658-8-88800-8-8800-4-4-44444-40002-22-200000000000000000000000000000000000000000000
χ661212-12-12-612-126-66-6600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-6-12126-666-600000000000000000000000000000000000000000000000000000000000
χ6812-1212-12-600-6660000000000000000000004i−4i000000000000000000000−2i2i000000000000000
χ6912-1212-12-600-666000000000000000000000−4i4i0000000000000000000002i−2i000000000000000
χ7012-12-1212-60066-600000000000000000000000000000000000000−2i32i3000000000000000000000
χ7112-12-1212-60066-6000000000000000000000000000000000000002i3−2i3000000000000000000000

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