Finite Group Databasebeta

← Group #13138067

Character table — Group #13138067

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order12223446661212336666664121236661212121244121212121212121212122224466888812122424242424242424266661212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111111111111-1-11111111111-111-1-1-1-111-1-1-1-1-1-1-1-11111-111-1-1-1-1
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111
χ511111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111
χ611111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111-1-1
χ811111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111-1-11111
χ92222222222222-12-122-1-1222-1-1-1-12-1-122222-1-1-1-1-1-1-1-120000-1-10000-1-100000000200-1-100
χ102222222222222-12-122-1-1222-1-1-1-12-1-12-2-222-1-1-1-1-1-1-1-1-200001100001100000000-2001100
χ112222222222222-12-122-1-1-2-2-2-1-1-1-12-1-1222-2-211-1-1111120000-1-10000-1-100000000-2001100
χ122222222222222-12-122-1-1-2-2-2-1-1-1-12-1-12-2-2-2-211-1-11111-200001100001100000000200-1-100
χ13222222222222-12-12-1-122222-1-1-1-1-122-100-1-122-1-1-1-1-1-102200002200000000-1-1-1-10-1-10000
χ14222222222222-12-12-1-122222-1-1-1-1-122-100-1-122-1-1-1-1-1-10-2-20000-2-20000000011110110000
χ15222222222222-12-12-1-122-2-2-2-1-1-1-1-122-10011-2-2-1-111110220000-2-20000000011110-1-10000
χ16222222222222-12-12-1-122-2-2-2-1-1-1-1-122-10011-2-2-1-111110-2-200002200000000-1-1-1-10110000
χ1722222-2-2222-2-2222222220002222-2-2-2-2220000-2-20000-20000-2-2000022000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-20000-2-2000020000220000-2-2000000000000000
χ1922222-2-2222-2-22-12-122-1-1000-1-1-1-1-211-22200−i3i311−i3−i3i3i3-20000110000-1-100000000000−i3i300
χ2022222-2-2222-2-22-12-122-1-1000-1-1-1-1-211-22200i3−i311i3i3−i3−i3-20000110000-1-100000000000i3−i300
χ2122222-2-2222-2-22-12-122-1-1000-1-1-1-1-211-2-2-200−i3i311−i3−i3i3i320000-1-100001100000000000i3−i300
χ2222222-2-2222-2-22-12-122-1-1000-1-1-1-1-211-2-2-200i3−i311i3i3−i3−i320000-1-100001100000000000−i3i300
χ2322-2-22002-2-2002222-2-2-2-200022-2-200002i−2i00000000000000000−i2i22−22i−2i22−2−2−i2−i2i2i20000000
χ2422-2-22002-2-2002222-2-2-2-200022-2-200002i−2i00000000000000000i2−i2−222i−2i−2−222i2i2−i2−i20000000
χ2522-2-22002-2-2002222-2-2-2-200022-2-20000−2i2i00000000000000000−i2i2−22−2i2i−2−222−i2−i2i2i20000000
χ2622-2-22002-2-2002222-2-2-2-200022-2-20000−2i2i00000000000000000i2−i22−2−2i2i22−2−2i2i2−i2−i20000000
χ272-2-2222-2-2-222-222-2-22-2-220002-22-2-22-220000002-200000002-20000000000000000000002-2
χ282-2-2222-2-2-222-222-2-22-2-220002-22-2-22-220000002-20000000-22000000000000000000000-22
χ292-2-222-22-2-22-2222-2-22-2-220002-22-22-22-2000000-22000002-200000000000000000002-20000
χ302-2-222-22-2-22-2222-2-22-2-220002-22-22-22-2000000-2200000-220000000000000000000-220000
χ312-2-222-22-2-22-22-121-2-11-22000-11-11-1-221003−3001-13−33−302-2000000000000003−33−30-110000
χ322-2-222-22-2-22-22-121-2-11-22000-11-11-1-221003−3001-13−33−30-2200000000000000−33−3301-10000
χ332-2-222-22-2-22-22-121-2-11-22000-11-11-1-22100−33001-1−33−3302-200000000000000−33−330-110000
χ342-2-222-22-2-22-22-121-2-11-22000-11-11-1-22100−33001-1−33−330-22000000000000003−33−301-10000
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
χ3744444-4-4444-4-4-24-24-2-244000-2-2-2-22-4-420000002200000000000000000000000000000000
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
χ4044-4-44004-4-4004-24-2-4-422000-2-22200004i−4i000000000000000000000−2i2i000000000000000
χ4144-4-44004-4-4004-24-2-4-422000-2-2220000−4i4i0000000000000000000002i−2i000000000000000
χ4244-4-44004-4-400-24-2422-4-4000-2-22200000000000000000000000−2i22i200000000i2i2−i2−i20000000
χ4344-4-44004-4-400-24-2422-4-4000-2-222000000000000000000000002i2−2i200000000−i2−i2i2i20000000
χ444-44-4400-44-40044-4-4-444-40004-4-4400000000000000000000000000000000000000000000
χ454-44-4400-44-4004-2-42-44-22000-222-2000000000000000000000−2i32i3000000000000000000000
χ464-44-4400-44-4004-2-42-44-22000-222-20000000000000000000002i3−2i3000000000000000000000
χ474-44-4400-44-400-242-42-24-4000-222-2000000000000000000000000000000000i6−i6−i6i60000000
χ484-44-4400-44-400-242-42-24-4000-222-2000000000000000000000000000000000−i6i6i6−i60000000
χ494-4-4444-4-4-444-44-2-424-42-2000-22-22-4-224000000-2200000000000000000000000000000000
χ504-4-4444-4-4-444-4-242-4-22-44000-22-2224-4-2000000-2200000000000000000000000000000000
χ514-4-4444-4-4-444-4-2-222-222-20001-11-12-22-20000001-13i−3i−3i3i0000000000000000000000000000
χ524-4-4444-4-4-444-4-2-222-222-20001-11-12-22-20000001-1−3i3i3i−3i0000000000000000000000000000
χ534-4-444-44-4-44-444-2-424-42-2000-22-2242-2-40000002-200000000000000000000000000000000
χ544-4-444-44-4-44-44-2-222-222-20001-11-1-22-220023−2300-11−33−330000000000000000000000000000
χ554-4-444-44-4-44-44-2-222-222-20001-11-1-22-2200−232300-113−33−30000000000000000000000000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000000002200002200-1-1-1-1000000000-1-1
χ576666-366-3-3-3-3-3000000006-3-300000000000000000000000-2-20000-2-200111100000000011
χ586666-366-3-3-3-3-300000000-63300000000000000000000000220000-2-2001111000000000-1-1
χ596666-366-3-3-3-3-300000000-63300000000000000000000000-2-200002200-1-1-1-100000000011
χ606-6-66-36-633-3-3300000000033−33000000000000000000000002-2000000003−33−3000000000-11
χ616-6-66-36-633-3-3300000000033−3300000000000000000000000-2200000000−33−330000000001-1
χ626-6-66-36-633-3-33000000000−3333000000000000000000000002-200000000−33−33000000000-11
χ636-6-66-36-633-3-33000000000−333300000000000000000000000-22000000003−33−30000000001-1
χ6488-8-88008-8-800-4-4-4-4444400022-2-200000000000000000000000000000000000000000000
χ658-88-8800-88-800-4-4444-4-440002-2-2200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-600-66600000000000000000000000000000000000000000022−2200−2−22200000000000
χ681212-12-12-600-666000000000000000000000000000000000000000000−22220022−2−200000000000
χ6912-1212-12-6006-6600000000000000000000000000000000000000000000006−6−6600000000000
χ7012-1212-12-6006-660000000000000000000000000000000000000000000000−666−600000000000
χ7112-12-1212-6-121266-66-600000000000000000000000000000000000000000000000000000000000

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