Finite Group Databasebeta

← Group #13140625

Character table — Group #13140625

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
χ31111111111111111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111
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
χ711111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-111
χ92222222222222-122-1-1-12222-1-1-1-12-1-122222-1-1-1-1-1-1-1-1002000000-1-1-1-1000000002-1-10000
χ102222222222222-122-1-1-12222-1-1-1-12-1-12-2-222-1-1-1-1-1-1-1-100-2000000111100000000-2110000
χ112222222222222-122-1-1-12-2-2-2-1-1-1-12-1-1222-2-2111111-1-1002000000-1-1-1-100000000-2110000
χ122222222222222-122-1-1-12-2-2-2-1-1-1-12-1-12-2-2-2-2111111-1-100-20000001111000000002-1-10000
χ13222222222222-12-1-1222-1222-1-1-1-1-122-100-1-122-1-1-1-1-1-100022002200000000-1-1-1-100000-1-1
χ14222222222222-12-1-1222-1222-1-1-1-1-122-100-1-122-1-1-1-1-1-1000-2-200-2-20000000011110000011
χ15222222222222-12-1-1222-1-2-2-2-1-1-1-1-122-10011-2-21111-1-10002200-2-200000000111100000-1-1
χ16222222222222-12-1-1222-1-2-2-2-1-1-1-1-122-10011-2-21111-1-1000-2-2002200000000-1-1-1-10000011
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
χ1922222-2-2222-2-22-122-1-1-12000-1-1-1-1-211-22200−i3i3−i3−i3i3i31100-2000000-1-111000000000−i3i30000
χ2022222-2-2222-2-22-122-1-1-12000-1-1-1-1-211-22200i3−i3i3i3−i3−i31100-2000000-1-111000000000i3−i30000
χ2122222-2-2222-2-22-122-1-1-12000-1-1-1-1-211-2-2-200−i3i3−i3−i3i3i31100200000011-1-1000000000i3−i30000
χ2222222-2-2222-2-22-122-1-1-12000-1-1-1-1-211-2-2-200i3−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−i2-2200−i2−i2i2i2i2i2−i2−i20000000
χ2622-2-22002-2-200222-2-22-2-200022-2-20000-22000000000000000i2−i2−i2i2-2200i2i2−i2−i2−i2−i2i2i20000000
χ272-22-222-2-2-222-222-222-2-2-20002-2-2222-2-200000000002-20002i−2i0000000000000000000002i−2i
χ282-22-222-2-2-222-222-222-2-2-20002-2-2222-2-200000000002-2000−2i2i000000000000000000000−2i2i
χ292-22-222-2-2-222-2-121-12-2-21000-111-1-12-2100−i3i300−i3i3−i3i3-110002i−2i0000000000003−33−300000−ii
χ302-22-222-2-2-222-2-121-12-2-21000-111-1-12-2100−i3i300−i3i3−i3i3-11000−2i2i000000000000−33−3300000i−i
χ312-22-222-2-2-222-2-121-12-2-21000-111-1-12-2100i3−i300i3−i3i3−i3-110002i−2i000000000000−33−3300000−ii
χ322-22-222-2-2-222-2-121-12-2-21000-111-1-12-2100i3−i300i3−i3i3−i3-11000−2i2i0000000000003−33−300000i−i
χ332-22-22-22-2-22-2222-222-2-2-20002-2-22-2-2220000000000-222-200000000000000000000002-200
χ342-22-22-22-2-22-2222-222-2-2-20002-2-22-2-2220000000000-22-220000000000000000000000-2200
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
χ3744444-4-4444-4-4-24-2-2444-2000-2-2-2-22-4-420000000000220000000000000000000000000000
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
χ4044-4-44004-4-4004-24-42-22-4000-2-22200004-40000000000000000000-2200000000000000000
χ4144-4-44004-4-4004-24-42-22-4000-2-2220000-4400000000000000000002-200000000000000000
χ4244-4-44004-4-400-24-22-44-42000-2-22200000000000000000000000−2i22i200000000i2i2−i2−i20000000
χ4344-4-44004-4-400-24-22-44-42000-2-222000000000000000000000002i2−2i200000000−i2−i2i2i20000000
χ444-44-444-4-4-444-44-2-44-222-4000-222-24-22-40000000000-220000000000000000000000000000
χ454-44-444-4-4-444-4-2-22-2-22220001-1-11-2-22200−2i32i300i3−i3i3−i31-10000000000000000000000000000
χ464-44-444-4-4-444-4-2-22-2-22220001-1-11-2-222002i3−2i300−i3i3−i3i31-10000000000000000000000000000
χ474-44-44-44-4-44-444-2-44-222-4000-222-2-42-2400000000002-20000000000000000000000000000
χ484-44-44-44-4-44-44-242-24-4-42000-222-22-44-200000000002-20000000000000000000000000000
χ494-44-44-44-4-44-44-2-22-2-22220001-1-1122-2-20000003-3-33-110000000000000000000000000000
χ504-44-44-44-4-44-44-2-22-2-22220001-1-1122-2-2000000-333-3-110000000000000000000000000000
χ514-4-44400-44-40044-4-4-4-4440004-44-400000000000000000000000000000000000000000000
χ524-4-44400-44-4004-2-4-422-24000-22-22000000000000000000000000000−2i32i3000000000000000
χ534-4-44400-44-4004-2-4-422-24000-22-220000000000000000000000000002i3−2i3000000000000000
χ544-4-44400-44-400-2422-4-44-2000-22-22000000000000000000000000000000000i6−i6−i6i60000000
χ554-4-44400-44-400-2422-4-44-2000-22-22000000000000000000000000000000000−i6i6i6−i60000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000002200022000000-1-1-1-10000000-1-100
χ576666-366-3-3-3-3-3000000006-3-300000000000000000000-2-2000-2-2000000111100000001100
χ586666-366-3-3-3-3-300000000-6330000000000000000000022000-2-200000011110000000-1-100
χ596666-366-3-3-3-3-300000000-63300000000000000000000-2-200022000000-1-1-1-100000001100
χ606-66-6-3-6633-33-3000000000−3i33i3000000000000000000002-200000000000−i3i3−i3i30000000-1100
χ616-66-6-3-6633-33-3000000000−3i33i300000000000000000000-2200000000000i3−i3i3−i300000001-100
χ626-66-6-3-6633-33-30000000003i3−3i3000000000000000000002-200000000000i3−i3i3−i30000000-1100
χ636-66-6-3-6633-33-30000000003i3−3i300000000000000000000-2200000000000−i3i3−i3i300000001-100
χ6488-8-88008-8-800-4-4-444-44400022-2-200000000000000000000000000000000000000000000
χ658-8-88800-88-800-4-44444-4-40002-22-200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-600-66600000000000000000000000000000000000000−2i22i2000000i2i2−i2−i200000000000
χ681212-12-12-600-666000000000000000000000000000000000000002i2−2i2000000−i2−i2i2i200000000000
χ6912-1212-12-612-1266-6-6600000000000000000000000000000000000000000000000000000000000
χ7012-12-1212-6006-6600000000000000000000000000000000000000000000006−6−6600000000000
χ7112-12-1212-6006-660000000000000000000000000000000000000000000000−666−600000000000

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