Finite Group Databasebeta

← Group #13140641

Character table — Group #13140641

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order1222344666121233666666266366612121212226666666612122222466888812122424242424242424466661212
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
χ511111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-1-1-11111-1-1-1-11-1-11111
χ92222222222222-122-1-12-1222-1-1-1-12-12-10022-1-1-1-1-1-1-1-100220000022000000-1-1-1-1000-1-100
χ102222222222222-122-1-12-1222-1-1-1-12-12-10022-1-1-1-1-1-1-1-100-2-200000-2-200000011110001100
χ112222222222222-122-1-12-1-2-2-2-1-1-1-12-12-100-2-2111111-1-1002200000-2-20000001111000-1-100
χ122222222222222-122-1-12-1-2-2-2-1-1-1-12-12-100-2-2111111-1-100-2-20000022000000-1-1-1-10001100
χ13222222222222-12-1-122-12222-1-1-1-1-12-1200-1-122-1-1-1-1-1-12200000220000-1-1-1-100000-1-10000
χ14222222222222-12-1-122-12222-1-1-1-1-12-1200-1-122-1-1-1-1-1-1-2-200000-2-20000111100000110000
χ15222222222222-12-1-122-12-2-2-2-1-1-1-1-12-120011-2-21111-1-12200000-2-20000111100000-1-10000
χ16222222222222-12-1-122-12-2-2-2-1-1-1-1-12-120011-2-21111-1-1-2-200000220000-1-1-1-100000110000
χ1722222-2-2222-2-2222222220002222-2-2-2-22200000000-2-20000-2220000-2-2000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-200000000-2-200002-2-2000022000000000000000
χ192-22-222-2-22-22-222-2-2-2-2220002-2-222-2-2200000000002-2002-2000000000000000000002-200
χ202-22-222-2-22-22-222-2-2-2-2220002-2-222-2-2200000000002-200-2200000000000000000000-2200
χ212-22-222-2-22-22-22-1-2-2112-1000-111-121-2-10000−i3i3−i3−i3i3i3-11002-20000000000000−i3−i3i3i3000-1100
χ222-22-222-2-22-22-22-1-2-2112-1000-111-121-2-10000−i3i3−i3−i3i3i3-1100-220000000000000i3i3−i3−i30001-100
χ232-22-222-2-22-22-22-1-2-2112-1000-111-121-2-10000i3−i3i3i3−i3−i3-11002-20000000000000i3i3−i3−i3000-1100
χ242-22-222-2-22-22-22-1-2-2112-1000-111-121-2-10000i3−i3i3i3−i3−i3-1100-220000000000000−i3−i3i3i30001-100
χ252-22-22-22-22-2-2222-2-2-2-2220002-2-22-222-20000000000-222-2000000000000000000002-20000
χ262-22-22-22-22-2-2222-2-2-2-2220002-2-22-222-20000000000-22-2200000000000000000000-220000
χ272-22-22-22-22-2-22-1211-2-2-12000-111-112-1-200−i3i300−i3i3−i3i31-12-200000000000−i3−i3i3i300000-110000
χ282-22-22-22-22-2-22-1211-2-2-12000-111-112-1-200−i3i300−i3i3−i3i31-1-2200000000000i3i3−i3−i3000001-10000
χ292-22-22-22-22-2-22-1211-2-2-12000-111-112-1-200i3−i300i3−i3i3−i31-12-200000000000i3i3−i3−i300000-110000
χ302-22-22-22-22-2-22-1211-2-2-12000-111-112-1-200i3−i300i3−i3i3−i31-1-2200000000000−i3−i3i3i3000001-10000
χ312-2-22200-2-2200222-22-2-2-200022-2-200002-20000000000000002-22−22−2002−22−22−22−20000000
χ322-2-22200-2-2200222-22-2-2-200022-2-200002-20000000000000002-2−22−2200−22−22−22−220000000
χ332-2-22200-2-2200222-22-2-2-200022-2-20000-22000000000000000-222−2−22002−22−2−22−220000000
χ342-2-22200-2-2200222-22-2-2-200022-2-20000-22000000000000000-22−222−200−22−222−22−20000000
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
χ3744444-4-4444-4-44-244-2-24-2000-2-2-2-2-42-420000000000220000000000000000000000000000
χ3844444-4-4444-4-4-24-2-244-24000-2-2-2-22-42-40000000000220000000000000000000000000000
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
χ4144-4-44004-4-40044-44-44-4-40004-44-400000000000000000000000000000000000000000000
χ4244-4-44004-4-4004-2-442-2-42000-22-22000000000000000000000000000000000i6−i6−i6i60000000
χ4344-4-44004-4-4004-2-442-2-42000-22-22000000000000000000000000000000000−i6i6i6−i60000000
χ4444-4-44004-4-400-242-2-442-4000-22-2200000000000000000000000000000i6−i6−i6i600000000000
χ4544-4-44004-4-400-242-2-442-4000-22-2200000000000000000000000000000−i6i6i6−i600000000000
χ464-44-444-4-44-44-4-2422-4-4-24000-222-2-2-4240000000000-220000000000000000000000000000
χ474-44-444-4-44-44-4-2-22222-2-20001-1-11-222-20000−2i32i3i3i3−i3−i31-10000000000000000000000000000
χ484-44-444-4-44-44-4-2-22222-2-20001-1-11-222-200002i3−2i3−i3−i3i3i31-10000000000000000000000000000
χ494-44-44-44-44-4-444-2-4-4224-2000-222-2-4-24200000000002-20000000000000000000000000000
χ504-44-44-44-44-4-44-2-22222-2-20001-1-112-2-2200−2i32i300i3−i3i3−i3-110000000000000000000000000000
χ514-44-44-44-44-4-44-2-22222-2-20001-1-112-2-22002i3−2i300−i3i3−i3i3-110000000000000000000000000000
χ524-4-44400-4-44004-24-4-22-42000-2-222000000000000000000000000022−22000000−22−220000000
χ534-4-44400-4-44004-24-4-22-42000-2-2220000000000000000000000000−22220000002−22−20000000
χ544-4-44400-4-4400-24-224-42-4000-2-2220000000000000000000000022−220000−22−2200000000000
χ554-4-44400-4-4400-24-224-42-4000-2-22200000000000000000000000−222200002−22−200000000000
χ566666-366-3-3-3-3-3000000006-3-30000000022000000000000002-1-10000-1-10000000020000-1-1
χ576666-366-3-3-3-3-3000000006-3-300000000-2-200000000000000-21100001100000000-2000011
χ586666-366-3-3-3-3-300000000-6330000000022000000000000002-1-10000-1-100000000-2000011
χ596666-366-3-3-3-3-300000000-63300000000-2-200000000000000-2110000110000000020000-1-1
χ606666-3-6-6-3-3-333000000000−3i33i3000000002200000000000000-2-1-10000110000000000000−i3i3
χ616666-3-6-6-3-3-333000000000−3i33i300000000-2-2000000000000002110000-1-10000000000000i3−i3
χ626666-3-6-6-3-3-3330000000003i3−3i3000000002200000000000000-2-1-10000110000000000000i3−i3
χ636666-3-6-6-3-3-3330000000003i3−3i300000000-2-2000000000000002110000-1-10000000000000−i3i3
χ6488-8-88008-8-800-4-44-44-4440002-22-200000000000000000000000000000000000000000000
χ658-8-88800-8-8800-4-4-44-444400022-2-200000000000000000000000000000000000000000000
χ661212-12-12-600-6660000000000000000000000000000000000000000000023−23000000000000000
χ671212-12-12-600-66600000000000000000000000000000000000000000000−2323000000000000000
χ6812-1212-12-612-126-66-6600000000000000000000000000000000000000000000000000000000000
χ6912-1212-12-6-12126-666-600000000000000000000000000000000000000000000000000000000000
χ7012-12-1212-60066-60000000000000000000004-4000000000000000-22000000000000000000000
χ7112-12-1212-60066-6000000000000000000000-440000000000000002-2000000000000000000000

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