Finite Group Databasebeta

← Group #13140534

Character table — Group #13140534

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order12223446661212336666662663666121212124466666666121244444888812121212242424242424242426612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1
χ511111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-111-1-11-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1
χ92222222222222-122-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1002000000-1-1-1-1000000002-1-10000
χ102222222222222-122-1-1-12222-1-1-1-1-1-122-2-222-1-1-1-1-1-1-1-100-2000000111100000000-2110000
χ112222222222222-122-1-1-12-2-2-2-1-1-1-1-1-12222-2-2111111-1-1002000000-1-1-1-100000000-2110000
χ122222222222222-122-1-1-12-2-2-2-1-1-1-1-1-122-2-2-2-2111111-1-100-20000001111000000002-1-10000
χ13222222222222-12-1-1222-1222-1-1-1-122-1-100-1-122-1-1-1-1-1-122000220000000000-1-1-1-100000-1-1
χ14222222222222-12-1-1222-1222-1-1-1-122-1-100-1-122-1-1-1-1-1-1-2-2000-2-2000000000011110000011
χ15222222222222-12-1-1222-1-2-2-2-1-1-1-122-1-10011-2-21111-1-122000-2-20000000000111100000-1-1
χ16222222222222-12-1-1222-1-2-2-2-1-1-1-122-1-10011-2-21111-1-1-2-2000220000000000-1-1-1-10000011
χ1722222-2-2222-2-2222222220002222-2-2-2-22200000000-2-200-200000022-2-2000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-200000000-2-2002000000-2-222000000000000000
χ1922222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-22200−i3i3−i3−i3i3i31100-2000000-1-111000000000−i3i30000
χ2022222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-22200i3−i3i3i3−i3−i31100-2000000-1-111000000000i3−i30000
χ2122222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-2-2-200−i3i3−i3−i3i3i31100200000011-1-1000000000i3−i30000
χ2222222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-2-2-200i3−i3i3i3−i3−i31100200000011-1-1000000000−i3i30000
χ2322-2-22002-2-200222-2-22-2-200022-2-200002-2000000000000000−i2i2−i2i22-200−i2−i2i2i2−i2−i2i2i20000000
χ2422-2-22002-2-200222-2-22-2-200022-2-200002-2000000000000000i2−i2i2−i22-200i2i2−i2−i2i2i2−i2−i20000000
χ2522-2-22002-2-200222-2-22-2-200022-2-20000-22000000000000000−i2i2i2−i2-2200i2i2−i2−i2−i2−i2i2i20000000
χ2622-2-22002-2-200222-2-22-2-200022-2-20000-22000000000000000i2−i2−i2i2-2200−i2−i2i2i2i2i2−i2−i20000000
χ272-22-222-2-22-22-222-2-22-2-220002-2-222-22-200000000002-20002i−2i00000000000000000002i−2i00
χ282-22-222-2-22-22-222-2-22-2-220002-2-222-22-200000000002-2000−2i2i0000000000000000000−2i2i00
χ292-22-22-22-22-2-2222-2-22-2-220002-2-22-22-220000000000-222-20000000000000000000000002-2
χ302-22-22-22-22-2-2222-2-22-2-220002-2-22-22-220000000000-22-22000000000000000000000000-22
χ312-22-22-22-22-2-22-12112-2-2-1000-111-1-221-100−i3i300−i3i3−i3i31-12-2000000000000000−i3i3−i3i300000-11
χ322-22-22-22-22-2-22-12112-2-2-1000-111-1-221-100−i3i300−i3i3−i3i31-1-22000000000000000i3−i3i3−i3000001-1
χ332-22-22-22-22-2-22-12112-2-2-1000-111-1-221-100i3−i300i3−i3i3−i31-12-2000000000000000i3−i3i3−i300000-11
χ342-22-22-22-22-2-22-12112-2-2-1000-111-1-221-100i3−i300i3−i3i3−i31-1-22000000000000000−i3i3−i3i3000001-1
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
χ3744444-4-4444-4-4-24-2-2444-2000-2-2-2-2-4-4220000000000220000000000000000000000000000
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
χ4044-4-44004-4-4004-24-42-22-4000-2-22200004-40000000000000000000-2200000000000000000
χ4144-4-44004-4-4004-24-42-22-4000-2-2220000-4400000000000000000002-200000000000000000
χ4244-4-44004-4-400-24-22-44-42000-2-222000000000000000000000−2i22i20000000000i2i2−i2−i20000000
χ4344-4-44004-4-400-24-22-44-42000-2-2220000000000000000000002i2−2i20000000000−i2−i2i2i20000000
χ444-44-444-4-44-44-44-2-4-4-2224000-222-2-224-40000000000-220000000000000000000000000000
χ454-44-444-4-44-44-4-24224-4-4-2000-222-24-4-220000000000-220000000000000000000000000000
χ464-44-444-4-44-44-4-2-222-222-20001-1-11-22-220000003-3-331-10000000000000000000000000000
χ474-44-444-4-44-44-4-2-222-222-20001-1-11-22-22000000-333-31-10000000000000000000000000000
χ484-44-44-44-44-4-444-2-4-4-2224000-222-22-2-4400000000002-20000000000000000000000000000
χ494-44-44-44-44-4-44-2-222-222-20001-1-112-22-200−2i32i300i3−i3i3−i3-110000000000000000000000000000
χ504-44-44-44-44-4-44-2-222-222-20001-1-112-22-2002i3−2i300−i3i3−i3i3-110000000000000000000000000000
χ514-4-44400-4-440044-44-4-44-40004-44-400000000000000000000000000000000000000000000
χ524-4-44400-4-44004-2-4422-2-4000-22-22000000000000000000000000000−2i32i3000000000000000
χ534-4-44400-4-44004-2-4422-2-4000-22-220000000000000000000000000002i3−2i3000000000000000
χ544-4-44400-4-4400-242-2-4-442000-22-220000000000000000000000000000000006−6−660000000
χ554-4-44400-4-4400-242-2-4-442000-22-22000000000000000000000000000000000−666−60000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000000002200220000-1-1-1-10000000-1-100
χ576666-366-3-3-3-3-3000000006-3-300000000000000000000000-2-200-2-20000111100000001100
χ586666-366-3-3-3-3-300000000-633000000000000000000000002200-2-2000011110000000-1-100
χ596666-366-3-3-3-3-300000000-63300000000000000000000000-2-200220000-1-1-1-100000001100
χ606-66-6-36-63-33-33000000000−3i33i3000000000000000000000002i−2i000000003−33−30000000−ii00
χ616-66-6-36-63-33-33000000000−3i33i300000000000000000000000−2i2i00000000−33−330000000i−i00
χ626-66-6-36-63-33-330000000003i3−3i3000000000000000000000002i−2i00000000−33−330000000−ii00
χ636-66-6-36-63-33-330000000003i3−3i300000000000000000000000−2i2i000000003−33−30000000i−i00
χ6488-8-88008-8-800-4-4-444-44400022-2-200000000000000000000000000000000000000000000
χ658-8-88800-8-8800-4-44-444-440002-22-200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-600-6660000000000000000000000000000000000000000−2i22i20000i2i2−i2−i200000000000
χ681212-12-12-600-66600000000000000000000000000000000000000002i2−2i20000−i2−i2i2i200000000000
χ6912-1212-12-6-12126-666-600000000000000000000000000000000000000000000000000000000000
χ7012-12-1212-60066-60000000000000000000000000000000000000000000000i6−i6−i6i600000000000
χ7112-12-1212-60066-60000000000000000000000000000000000000000000000−i6i6i6−i600000000000

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