Finite Group Databasebeta

← Group #13140609

Character table — Group #13140609

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222224466666666888121212121212121224242424242424242424363636363636363636363636363636363636727272727272727272
order122234466612123366666626636661212121266666666121224668888121224242424242424242446612121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-111-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-1-1-1-111
χ511111111111111111111-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-1111-1-111
χ711111111111111111111-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-11111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-11111-1-1
χ92222222222222-12-12-12-1222-1-1-1-12-1-1222-1-1-1-1-1-1-1-122-1-10000-1-10000000002000-1-100
χ102222222222222-12-12-12-1222-1-1-1-12-1-1222-1-1-1-1-1-1-1-1-2-211000011000000000-20001100
χ112222222222222-12-12-12-1-2-2-2-1-1-1-12-1-12-2-2111111-1-122-1-10000-1-1000000000-20001100
χ122222222222222-12-12-12-1-2-2-2-1-1-1-12-1-12-2-2111111-1-1-2-2110000110000000002000-1-100
χ13222222222222-12-12-12-12222-1-1-1-1-122-1-1-122-1-1-1-1-1-100000022000000-1-1-1-10020000-1-1
χ14222222222222-12-12-12-12222-1-1-1-1-122-1-1-122-1-1-1-1-1-1000000-2-2000000111100-2000011
χ15222222222222-12-12-12-12-2-2-2-1-1-1-1-122-111-2-21111-1-100000022000000-1-1-1-100-2000011
χ16222222222222-12-12-12-12-2-2-2-1-1-1-1-122-111-2-21111-1-1000000-2-200000011110020000-1-1
χ1722222-2-2222-2-2222222220002222-2-2-2-200000000-2-22-2220000-2-200000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-200000000-2-2-22-2-200002200000000000000000
χ1922222-2-2222-2-22-12-12-12-1000-1-1-1-1-211-200−i3i3−i3−i3i3i3112-2-1-10000110000000000000−i3i300
χ2022222-2-2222-2-22-12-12-12-1000-1-1-1-1-211-200−i3i3−i3−i3i3i311-22110000-1-10000000000000i3−i300
χ2122222-2-2222-2-22-12-12-12-1000-1-1-1-1-211-200i3−i3i3i3−i3−i3112-2-1-10000110000000000000i3−i300
χ2222222-2-2222-2-22-12-12-12-1000-1-1-1-1-211-200i3−i3i3i3−i3−i311-22110000-1-10000000000000−i3i300
χ2322-2-222-2-2-222-222-2-222-2-20002-2-2222-2-2000000002-20000002i−2i0000002i2i−2i−2i000000000
χ2422-2-222-2-2-222-222-2-222-2-20002-2-2222-2-2000000002-2000000−2i2i000000−2i−2i2i2i000000000
χ2522-2-222-2-2-222-2-121-2-121-2000-111-1-12-21−i3i300−i3i3−i3i3-110000002i−2i000000−i−iii00000003−3
χ2622-2-222-2-2-222-2-121-2-121-2000-111-1-12-21−i3i300−i3i3−i3i3-11000000−2i2i000000ii−i−i0000000−33
χ2722-2-222-2-2-222-2-121-2-121-2000-111-1-12-21i3−i300i3−i3i3−i3-110000002i−2i000000−i−iii0000000−33
χ2822-2-222-2-2-222-2-121-2-121-2000-111-1-12-21i3−i300i3−i3i3−i3-11000000−2i2i000000ii−i−i00000003−3
χ2922-2-22-22-2-22-2222-2-222-2-20002-2-22-2-22200000000-2200002-2000022-2-20000000000000
χ3022-2-22-22-2-22-2222-2-222-2-20002-2-22-2-22200000000-220000-220000-2-2220000000000000
χ31444444444444-2-2-2-2-2-2-2-24441111-2-2-2-2-2-2-2-2111111000000000000000000000000000
χ32444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-22222-1-1-1-111000000000000000000000000000
χ3344444-4-4444-4-4-24-24-24-24000-2-2-2-22-4-420000000022000000000000000000000000000
χ3444444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200−2i32i3i3i3−i3−i3-1-1000000000000000000000000000
χ3544444-4-4444-4-4-2-2-2-2-2-2-2-200011112222002i3−2i3−i3−i3i3i3-1-1000000000000000000000000000
χ3644-4-444-4-4-444-44-2-424-2-42000-222-24-22-400000000-22000000000000000000000000000
χ3744-4-444-4-4-444-4-2-222-2-2220001-1-11-2-222−2i32i300i3−i3i3−i31-1000000000000000000000000000
χ3844-4-444-4-4-444-4-2-222-2-2220001-1-11-2-2222i3−2i300−i3i3−i3i31-1000000000000000000000000000
χ3944-4-44-44-4-44-444-2-424-2-42000-222-2-42-24000000002-2000000000000000000000000000
χ4044-4-44-44-4-44-44-242-4-242-4000-222-22-44-2000000002-2000000000000000000000000000
χ4144-4-44-44-4-44-44-2-222-2-2220001-1-1122-2-200003-3-33-11000000000000000000000000000
χ4244-4-44-44-4-44-44-2-222-2-2220001-1-1122-2-20000-333-3-11000000000000000000000000000
χ434-44-44004-4-400444-4-4-4-4400044-4-400000000000000000000000000000000000000000
χ444-44-44004-4-4004-242-42-4-2000-2-2220000000000000000−2i32i300000000000000000000000
χ454-44-44004-4-4004-242-42-4-2000-2-22200000000000000002i3−2i300000000000000000000000
χ464-44-44004-4-400-24-2-42-424000-2-22200000000000000000000000000006−66−6000000000
χ474-44-44004-4-400-24-2-42-424000-2-2220000000000000000000000000000−66−66000000000
χ484-4-44400-44-40044-44-4-44-40004-44-400000000000000000000000000000000000000000
χ494-4-44400-44-4004-2-4-2-4242000-22-22000000000000000000000023−2300000000000000000
χ504-4-44400-44-4004-2-4-2-4242000-22-220000000000000000000000−232300000000000000000
χ514-4-44400-44-400-24242-4-2-4000-22-220000000000000000000000000000i6−i6−i6i6000000000
χ524-4-44400-44-400-24242-4-2-4000-22-220000000000000000000000000000−i6i6i6−i6000000000
χ536666-366-3-3-3-3-3000000006-3-30000000000000000000000220000-1-1-1-10000200-1-10000
χ546666-366-3-3-3-3-3000000006-3-30000000000000000000000-2-2000011110000-200110000
χ556666-366-3-3-3-3-300000000-6330000000000000000000000220000-1-1-1-10000-200110000
χ566666-366-3-3-3-3-300000000-6330000000000000000000000-2-2000011110000200-1-10000
χ5766-6-6-3-6633-33-3000000000−3i33i300000000000000000000002-20000-1-1110000000−i3i30000
χ5866-6-6-3-6633-33-3000000000−3i33i30000000000000000000000-22000011-1-10000000i3−i30000
χ5966-6-6-3-6633-33-30000000003i3−3i300000000000000000000002-20000-1-1110000000i3−i30000
χ6066-6-6-3-6633-33-30000000003i3−3i30000000000000000000000-22000011-1-10000000−i3i30000
χ618-88-88008-8-800-4-4-44444-400022-2-200000000000000000000000000000000000000000
χ628-8-88800-88-800-4-44-444-440002-22-200000000000000000000000000000000000000000
χ6312121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000
χ641212-12-12-612-1266-6-6600000000000000000000000000000000000000000000000000000000
χ6512-1212-12-600-66600000000000000000000000000000000000000000i6−i6i6−i60000000000000
χ6612-1212-12-600-66600000000000000000000000000000000000000000−i6i6−i6i60000000000000
χ6712-12-1212-6006-6600000000000000000000000000000000000000000i6−i6−i6i60000000000000
χ6812-12-1212-6006-6600000000000000000000000000000000000000000−i6i6i6−i60000000000000

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