Finite Group Databasebeta

← Group #13140918

Character table — Group #13140918

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222224466666666888121212121212121224242424242424242424363636363636363636363636363636363636727272727272727272
order1222344666121233666666412123666121212121212121212121212121224668888121224242424242424242446612121212
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
χ511111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-111111-1-1
χ711111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-11111
χ92222222222222-12-1-1-122222-1-1-1-1-122-1-1-122-1-1-1-1-1-100000022000000-1-1-1-1200-1-10000
χ102222222222222-12-1-1-122222-1-1-1-1-122-1-1-122-1-1-1-1-1-1000000-2-20000001111-200110000
χ112222222222222-12-1-1-122-2-2-2-1-1-1-1-122-111-2-2-1-1111100000022000000-1-1-1-1-200110000
χ122222222222222-12-1-1-122-2-2-2-1-1-1-1-122-111-2-2-1-11111000000-2-20000001111200-1-10000
χ13222222222222-12-1222-1-1222-1-1-1-12-1-1222-1-1-1-1-1-1-1-122-1-10000-1-1000000000200000-1-1
χ14222222222222-12-1222-1-1222-1-1-1-12-1-1222-1-1-1-1-1-1-1-1-2-211000011000000000-20000011
χ15222222222222-12-1222-1-1-2-2-2-1-1-1-12-1-12-2-211-1-1111122-1-10000-1-1000000000-20000011
χ16222222222222-12-1222-1-1-2-2-2-1-1-1-12-1-12-2-211-1-11111-2-211000011000000000200000-1-1
χ1722222-2-2222-2-2222222220002222-2-2-2-20000-2-200002-2220000-2-200000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-20000-2-20000-22-2-200002200000000000000000
χ1922222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-200−i3i311−i3−i3i3i32-2-1-1000011000000000000000−i3i3
χ2022222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-200−i3i311−i3−i3i3i3-22110000-1-1000000000000000i3−i3
χ2122222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-200i3−i311i3i3−i3−i32-2-1-1000011000000000000000i3−i3
χ2222222-2-2222-2-2-12-1222-1-1000-1-1-1-1-211-200i3−i311i3i3−i3−i3-22110000-1-1000000000000000−i3i3
χ232-22-222-2-22-22-222-2-2-222-20002-2-2222-2-200002-2000000002i−2i00002i2i−2i−2i0000000000000
χ242-22-222-2-22-22-222-2-2-222-20002-2-2222-2-200002-200000000−2i2i0000−2i−2i2i2i0000000000000
χ252-22-22-22-22-2-2222-2-2-222-20002-2-22-2-2220000-2200000000002-200000022-2-2000000000
χ262-22-22-22-22-2-2222-2-2-222-20002-2-22-2-2220000-220000000000-22000000-2-222000000000
χ272-22-22-22-22-2-222-1-211-12-2000-111-11-22-1−i3i3001-1−i3i3−i3i30000002-2000000-1-111000−i3i30000
χ282-22-22-22-22-2-222-1-211-12-2000-111-11-22-1−i3i3001-1−i3i3−i3i3000000-2200000011-1-1000i3−i30000
χ292-22-22-22-22-2-222-1-211-12-2000-111-11-22-1i3−i3001-1i3−i3i3−i30000002-2000000-1-111000i3−i30000
χ302-22-22-22-22-2-222-1-211-12-2000-111-11-22-1i3−i3001-1i3−i3i3−i3000000-2200000011-1-1000−i3i30000
χ31444444444444-2-2-2-2-2-2-2-24441111-2-2-2-2-2-2-2-2111111000000000000000000000000000
χ32444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-2222211-1-1-1-1000000000000000000000000000
χ3344444-4-4444-4-44-24-2-2-244000-2-2-2-22-4-420000220000000000000000000000000000000
χ3444444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200−2i32i3-1-1i3i3−i3−i3000000000000000000000000000
χ3544444-4-4444-4-4-2-2-2-2-2-2-2-200011112222002i3−2i3-1-1−i3−i3i3i3000000000000000000000000000
χ3644-4-44004-4-4004444-4-4-4-400044-4-400000000000000000000000000000000000000000
χ3744-4-44004-4-4004-24-222-4-4000-2-22200000000000000000000000000006−66−6000000000
χ3844-4-44004-4-4004-24-222-4-4000-2-2220000000000000000000000000000−66−66000000000
χ3944-4-44004-4-400-24-24-4-422000-2-2220000000000000000−2i32i300000000000000000000000
χ4044-4-44004-4-400-24-24-4-422000-2-22200000000000000002i3−2i300000000000000000000000
χ414-44-444-4-44-44-44-2-422-24-4000-222-2-24-420000-220000000000000000000000000000000
χ424-44-444-4-44-44-4-242-4-44-22000-222-24-22-40000-220000000000000000000000000000000
χ434-44-444-4-44-44-4-2-2222-2-220001-1-11-2-22200001-13-3-33000000000000000000000000000
χ444-44-444-4-44-44-4-2-2222-2-220001-1-11-2-22200001-1-333-3000000000000000000000000000
χ454-44-44-44-44-4-44-242-4-44-22000-222-2-42-2400002-20000000000000000000000000000000
χ464-44-44-44-44-4-44-2-2222-2-220001-1-1122-2-2−2i32i300-11i3−i3i3−i3000000000000000000000000000
χ474-44-44-44-44-4-44-2-2222-2-220001-1-1122-2-22i3−2i300-11−i3i3−i3i3000000000000000000000000000
χ484-4-44400-4-440044-4-44-4-440004-44-400000000000000000000000000000000000000000
χ494-4-44400-4-44004-2-42-22-44000-22-2200000000000000000000000000006−6−66000000000
χ504-4-44400-4-44004-2-42-22-44000-22-220000000000000000000000000000−666−6000000000
χ514-4-44400-4-4400-242-44-42-2000-22-22000000000000000000000023−2300000000000000000
χ524-4-44400-4-4400-242-44-42-2000-22-220000000000000000000000−232300000000000000000
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
χ576-66-6-36-63-33-33000000000−3i33i300000000000000000000002i−2i0000−i−iii0000000003−300
χ586-66-6-36-63-33-33000000000−3i33i30000000000000000000000−2i2i0000ii−i−i000000000−3300
χ596-66-6-36-63-33-330000000003i3−3i300000000000000000000002i−2i0000−i−iii000000000−3300
χ606-66-6-36-63-33-330000000003i3−3i30000000000000000000000−2i2i0000ii−i−i0000000003−300
χ6188-8-88008-8-800-4-4-4-4444400022-2-200000000000000000000000000000000000000000
χ628-8-88800-8-8800-4-444-444-40002-22-200000000000000000000000000000000000000000
χ6312121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000
χ641212-12-12-600-66600000000000000000000000000000000000000000i6−i6i6−i60000000000000
χ651212-12-12-600-66600000000000000000000000000000000000000000−i6i6−i6i60000000000000
χ6612-1212-12-6-12126-666-600000000000000000000000000000000000000000000000000000000
χ6712-12-1212-60066-6000000000000000000000000000000000000000006−6−660000000000000
χ6812-12-1212-60066-600000000000000000000000000000000000000000−666−60000000000000

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