Finite Group Databasebeta

← Group #13140558

Character table — Group #13140558

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222224466666666888121212121212121224242424242424242424363636363636363636363636363636363636727272727272727272
order122234466612123366666626636661212121266666666121224668888121224242424242424242446612121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-111
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-1-111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111-1-111-1-1-1-1
χ511111111111111111111-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-111111-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-11111
χ92222222222222-12-1-1-122222-1-1-1-1-122-122-1-1-1-1-1-1-1-100000022000000-1-1-1-1200-1-10000
χ102222222222222-12-1-1-122222-1-1-1-1-122-122-1-1-1-1-1-1-1-1000000-2-20000001111-200110000
χ112222222222222-12-1-1-122-2-2-2-1-1-1-1-122-1-2-2111111-1-100000022000000-1-1-1-1-200110000
χ122222222222222-12-1-1-122-2-2-2-1-1-1-1-122-1-2-2111111-1-1000000-2-20000001111200-1-10000
χ13222222222222-12-1222-1-1222-1-1-1-12-1-12-1-122-1-1-1-1-1-122-1-10000-1-1000000000200000-1-1
χ14222222222222-12-1222-1-1222-1-1-1-12-1-12-1-122-1-1-1-1-1-1-2-211000011000000000-20000011
χ15222222222222-12-1222-1-1-2-2-2-1-1-1-12-1-1211-2-21111-1-122-1-10000-1-1000000000-20000011
χ16222222222222-12-1222-1-1-2-2-2-1-1-1-12-1-1211-2-21111-1-1-2-211000011000000000200000-1-1
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
χ1922222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-2−i3i300−i3−i3i3i3112-2-1-1000011000000000000000−i3i3
χ2022222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-2−i3i300−i3−i3i3i311-22110000-1-1000000000000000i3−i3
χ2122222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-2i3−i300i3i3−i3−i3112-2-1-1000011000000000000000i3−i3
χ2222222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-2i3−i300i3i3−i3−i311-22110000-1-1000000000000000−i3i3
χ2322-2-222-2-22-22-222-2-2-222-20002-2-2222-2-2000000002-200002i−2i00002i2i−2i−2i0000000000000
χ2422-2-222-2-22-22-222-2-2-222-20002-2-2222-2-2000000002-20000−2i2i0000−2i−2i2i2i0000000000000
χ2522-2-22-22-22-2-2222-2-2-222-20002-2-22-2-22200000000-220000002-200000022-2-2000000000
χ2622-2-22-22-22-2-2222-2-2-222-20002-2-22-2-22200000000-22000000-22000000-2-222000000000
χ2722-2-22-22-22-2-222-1-211-12-2000-111-11-22-100−i3i3−i3i3−i3i31-10000002-2000000-1-111000−i3i30000
χ2822-2-22-22-22-2-222-1-211-12-2000-111-11-22-100−i3i3−i3i3−i3i31-1000000-2200000011-1-1000i3−i30000
χ2922-2-22-22-22-2-222-1-211-12-2000-111-11-22-100i3−i3i3−i3i3−i31-10000002-2000000-1-111000i3−i30000
χ3022-2-22-22-22-2-222-1-211-12-2000-111-11-22-100i3−i3i3−i3i3−i31-1000000-2200000011-1-1000−i3i30000
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
χ3344444-4-4444-4-44-24-2-2-244000-2-2-2-22-4-420000000022000000000000000000000000000
χ3444444-4-4444-4-4-2-2-2-2-2-2-2-200011112222−2i32i300i3i3−i3−i3-1-1000000000000000000000000000
χ3544444-4-4444-4-4-2-2-2-2-2-2-2-2000111122222i3−2i300−i3−i3i3i3-1-1000000000000000000000000000
χ3644-4-444-4-44-44-44-2-422-24-4000-222-2-24-4200000000-22000000000000000000000000000
χ3744-4-444-4-44-44-4-242-4-44-22000-222-24-22-400000000-22000000000000000000000000000
χ3844-4-444-4-44-44-4-2-2222-2-220001-1-11-2-22200003-3-331-1000000000000000000000000000
χ3944-4-444-4-44-44-4-2-2222-2-220001-1-11-2-2220000-333-31-1000000000000000000000000000
χ4044-4-44-44-44-4-44-242-4-44-22000-222-2-42-24000000002-2000000000000000000000000000
χ4144-4-44-44-44-4-44-2-2222-2-220001-1-1122-2-200−2i32i3i3−i3i3−i3-11000000000000000000000000000
χ4244-4-44-44-44-4-44-2-2222-2-220001-1-1122-2-2002i3−2i3−i3i3−i3i3-11000000000000000000000000000
χ434-44-44004-4-40044-44-4-4-4400044-4-400000000000000000000000000000000000000000
χ444-44-44004-4-4004-2-4-222-44000-2-2220000000000000000000000000000i6−i6i6−i6000000000
χ454-44-44004-4-4004-2-4-222-44000-2-2220000000000000000000000000000−i6i6−i6i6000000000
χ464-44-44004-4-400-2424-4-42-2000-2-2220000000000000000−2i32i300000000000000000000000
χ474-44-44004-4-400-2424-4-42-2000-2-22200000000000000002i3−2i300000000000000000000000
χ484-4-44400-4-4400444-44-4-4-40004-44-400000000000000000000000000000000000000000
χ494-4-44400-4-44004-242-22-4-4000-22-220000000000000000000000000000i6−i6−i6i6000000000
χ504-4-44400-4-44004-242-22-4-4000-22-220000000000000000000000000000−i6i6i6−i6000000000
χ514-4-44400-4-4400-24-2-44-422000-22-22000000000000000000000023−2300000000000000000
χ524-4-44400-4-4400-24-2-44-422000-22-220000000000000000000000−232300000000000000000
χ536666-366-3-3-3-3-3000000006-3-30000000000000000000000220000-1-1-1-1000000200-1-100
χ546666-366-3-3-3-3-3000000006-3-30000000000000000000000-2-200001111000000-2001100
χ556666-366-3-3-3-3-300000000-6330000000000000000000000220000-1-1-1-1000000-2001100
χ566666-366-3-3-3-3-300000000-6330000000000000000000000-2-200001111000000200-1-100
χ5766-6-6-36-63-33-33000000000−3i33i300000000000000000000002i−2i0000−i−iii0000000003−300
χ5866-6-6-36-63-33-33000000000−3i33i30000000000000000000000−2i2i0000ii−i−i000000000−3300
χ5966-6-6-36-63-33-330000000003i3−3i300000000000000000000002i−2i0000−i−iii000000000−3300
χ6066-6-6-36-63-33-330000000003i3−3i30000000000000000000000−2i2i0000ii−i−i0000000003−300
χ618-88-88008-8-800-4-44-4444-400022-2-200000000000000000000000000000000000000000
χ628-8-88800-8-8800-4-4-44-44440002-22-200000000000000000000000000000000000000000
χ6312121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000
χ641212-12-12-6-12126-666-600000000000000000000000000000000000000000000000000000000
χ6512-1212-12-600-666000000000000000000000000000000000000000006−66−60000000000000
χ6612-1212-12-600-66600000000000000000000000000000000000000000−66−660000000000000
χ6712-12-1212-60066-600000000000000000000000000000000000000000i6−i6−i6i60000000000000
χ6812-12-1212-60066-600000000000000000000000000000000000000000−i6i6i6−i60000000000000

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