Finite Group Databasebeta

← Group #13140549

Character table — Group #13140549

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order12223446661212336666662663666121212124466666666121224444668888121224242424242424244121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111111111111-1-11111111111-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1
χ511111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111
χ611111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111-1-11111-1-1-1-11-1-11111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1
χ92222222222222-12-12-12-1222-1-1-1-12-1-122222-1-1-1-1-1-1-1-120000-1-10000-1-100000000200-1-100
χ102222222222222-12-12-12-1222-1-1-1-12-1-12-2-222-1-1-1-1-1-1-1-1-200001100001100000000-2001100
χ112222222222222-12-12-12-1-2-2-2-1-1-1-12-1-1222-2-2111111-1-120000-1-10000-1-100000000-2001100
χ122222222222222-12-12-12-1-2-2-2-1-1-1-12-1-12-2-2-2-2111111-1-1-200001100001100000000200-1-100
χ13222222222222-12-12-12-12222-1-1-1-1-122-100-1-122-1-1-1-1-1-102200002200000000-1-1-1-100000-1-1
χ14222222222222-12-12-12-12222-1-1-1-1-122-100-1-122-1-1-1-1-1-10-2-20000-2-20000000011110000011
χ15222222222222-12-12-12-12-2-2-2-1-1-1-1-122-10011-2-21111-1-10220000-2-200000000111100000-1-1
χ16222222222222-12-12-12-12-2-2-2-1-1-1-1-122-10011-2-21111-1-10-2-200002200000000-1-1-1-10000011
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
χ1922222-2-2222-2-22-12-12-12-1000-1-1-1-1-211-22200−i3i3−i3−i3i3i311-20000110000-1-100000000000−i3i300
χ2022222-2-2222-2-22-12-12-12-1000-1-1-1-1-211-22200i3−i3i3i3−i3−i311-20000110000-1-100000000000i3−i300
χ2122222-2-2222-2-22-12-12-12-1000-1-1-1-1-211-2-2-200−i3i3−i3−i3i3i31120000-1-100001100000000000i3−i300
χ2222222-2-2222-2-22-12-12-12-1000-1-1-1-1-211-2-2-200i3−i3i3i3−i3−i31120000-1-100001100000000000−i3i300
χ2322-2-222-2-22-22-222-2-222-2-20002-2-22-22-2200000000002-20002i−2i000000000000000002i−2i0000
χ2422-2-222-2-22-22-222-2-222-2-20002-2-22-22-2200000000002-2000−2i2i00000000000000000−2i2i0000
χ2522-2-22-22-22-2-2222-2-222-2-20002-2-222-22-20000000000-2202i−2i000000000000000000000002i−2i
χ2622-2-22-22-22-2-2222-2-222-2-20002-2-222-22-20000000000-220−2i2i00000000000000000000000−2i2i
χ2722-2-22-22-22-2-22-121-2-121-2000-111-1-1-22100−i3i300−i3i3−i3i31-102i−2i0000000000000033−3−300000−ii
χ2822-2-22-22-22-2-22-121-2-121-2000-111-1-1-22100−i3i300−i3i3−i3i31-10−2i2i00000000000000−3−33300000i−i
χ2922-2-22-22-22-2-22-121-2-121-2000-111-1-1-22100i3−i300i3−i3i3−i31-102i−2i00000000000000−3−33300000−ii
χ3022-2-22-22-22-2-22-121-2-121-2000-111-1-1-22100i3−i300i3−i3i3−i31-10−2i2i0000000000000033−3−300000i−i
χ312-22-22002-2-20022-22-2-22-200022-2-200002i−2i000000000000000002−2−i2i22i−2i−i2−i2i2i22−22−20000000
χ322-22-22002-2-20022-22-2-22-200022-2-200002i−2i00000000000000000−22i2−i22i−2ii2i2−i2−i2−22−220000000
χ332-22-22002-2-20022-22-2-22-200022-2-20000−2i2i000000000000000002−2i2−i2−2i2ii2i2−i2−i22−22−20000000
χ342-22-22002-2-20022-22-2-22-200022-2-20000−2i2i00000000000000000−22−i2i2−2i2i−i2−i2i2i2−22−220000000
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
χ3744444-4-4444-4-4-24-24-24-24000-2-2-2-22-4-420000000000220000000000000000000000000000
χ3844444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000−2i32i3i3i3−i3−i3-1-10000000000000000000000000000
χ3944444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200002i3−2i3−i3−i3i3i3-1-10000000000000000000000000000
χ4044-4-444-4-44-44-44-2-424-2-42000-222-2-4-2240000000000-220000000000000000000000000000
χ4144-4-444-4-44-44-4-242-4-242-4000-222-224-4-20000000000-220000000000000000000000000000
χ4244-4-444-4-44-44-4-2-222-2-2220001-1-112-22-20000003-3-331-10000000000000000000000000000
χ4344-4-444-4-44-44-4-2-222-2-2220001-1-112-22-2000000-333-31-10000000000000000000000000000
χ4444-4-44-44-44-4-444-2-424-2-42000-222-242-2-400000000002-20000000000000000000000000000
χ4544-4-44-44-44-4-44-2-222-2-2220001-1-11-22-2200−2i32i300i3−i3i3−i3-110000000000000000000000000000
χ4644-4-44-44-44-4-44-2-222-2-2220001-1-11-22-22002i3−2i300−i3i3−i3i3-110000000000000000000000000000
χ474-44-44004-4-4004-2-4-2-4242000-2-22200004i−4i000000000000000000000−2i2i000000000000000
χ484-44-44004-4-4004-2-4-2-4242000-2-2220000−4i4i0000000000000000000002i−2i000000000000000
χ494-44-44004-4-400-24242-4-2-4000-2-2220000000000000000000000022−2200000000−22−220000000
χ504-44-44004-4-400-24242-4-2-4000-2-22200000000000000000000000−2222000000002−22−20000000
χ514-4-44400-4-4400444-4-4-4-440004-44-400000000000000000000000000000000000000000000
χ524-4-44400-4-44004-242-42-4-2000-22-22000000000000000000000−2i32i3000000000000000000000
χ534-4-44400-4-44004-242-42-4-2000-22-220000000000000000000002i3−2i3000000000000000000000
χ544-4-44400-4-4400-24-2-42-424000-22-220000000000000000000000000000000006−6−660000000
χ554-4-44400-4-4400-24-2-42-424000-22-22000000000000000000000000000000000−666−60000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000000002200002200-1-1-1-100000-1-10000
χ576666-366-3-3-3-3-3000000006-3-300000000000000000000000-2-20000-2-200111100000110000
χ586666-366-3-3-3-3-300000000-63300000000000000000000000220000-2-200111100000-1-10000
χ596666-366-3-3-3-3-300000000-63300000000000000000000000-2-200002200-1-1-1-100000110000
χ6066-6-6-36-63-33-33000000000−3i33i3000000000000000000000002i−2i000000003−33−300000−ii0000
χ6166-6-6-36-63-33-33000000000−3i33i300000000000000000000000−2i2i00000000−33−3300000i−i0000
χ6266-6-6-36-63-33-330000000003i3−3i3000000000000000000000002i−2i00000000−33−3300000−ii0000
χ6366-6-6-36-63-33-330000000003i3−3i300000000000000000000000−2i2i000000003−33−300000i−i0000
χ648-88-88008-8-800-4-44-444-4400022-2-200000000000000000000000000000000000000000000
χ658-8-88800-8-8800-4-4-44444-40002-22-200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-6-12126-666-600000000000000000000000000000000000000000000000000000000000
χ6812-1212-12-600-666000000000000000000000000000000000000000000−2i22i200i2i2−i2−i200000000000
χ6912-1212-12-600-6660000000000000000000000000000000000000000002i2−2i200−i2−i2i2i200000000000
χ7012-12-1212-60066-60000000000000000000000000000000000000000000000i6−i6−i6i600000000000
χ7112-12-1212-60066-60000000000000000000000000000000000000000000000−i6i6i6−i600000000000

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