Finite Group Databasebeta

← Group #13149487

Character table — Group #13149487

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12223446664412123366666612123666121212121212121222441212121212121212121212122244444444666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-11-1-11-1-111-111-1-1-1-1-1-1-1-1-1-111-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-11-111-1-11-1-1-1-1-1-11111-1-1-1-111-1-1
χ51111111111-1-11111111111-1-11111-1-111-1-11111111111-1-1-1-111-1-1-11-11-11-11-1-11111-1-11111-1-111-1-1-1-1
χ61111111111-1-11111111111-1-11111-1-111-1-11111111111-1-1-1-111-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-111-1111-1-111-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11111-1-11-1-1-1-1-111111111-1-1-1-111
χ911111-1-11111-1-1-111111111-11111111-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-111-1-1-11-1-111111111-1-111-1-1-1-11-1-11
χ1011111-1-11111-1-1-111111111-11111111-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-11-1-111-111-1-1-1-1111111-1-1-1-111-111-1
χ1111111-1-11111-1-1-111111111-11111111-1-1-1-1-1-1-1-11111111-111-1-1-1-1-1111-1-11-11-111-1-1-1-111-1-111-1-1-11-11
χ1211111-1-11111-1-1-111111111-11111111-1-1-1-1-1-1-1-11111111-111-1-1-1-1-1-11-111-11-11-1-1-1-1-1-1-1-11111111-11-1
χ1311111-1-1111-11-1-1111111111-11111-1-1-1-111-1-111-1-1-1-1-1-1-11-1-1-1-111-111-1111-1-1-11111-1-1-1-11111-1-1-111-1
χ1411111-1-1111-11-1-1111111111-11111-1-1-1-111-1-111-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1111-1-111-1-111-1-111111-1-11
χ1511111-1-1111-11-1-1111111111-11111-1-1-1-111-1-1-1-1111111-11-1-1-1-11111-111-1-1-1-1111-1-11111-1-1-1-1-1-11-11-1
χ1611111-1-1111-11-1-1111111111-11111-1-1-1-111-1-1-1-1111111-11-1-1-1-1111-1-1-1-11111-1-1-1-1-111-1-111-1-111-11-11
χ17222222222222222-12-1-12-1222-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1202000000000-1-1-1-10000-1-1000000
χ18222222222222222-12-1-12-1222-1-1-1-1-1-1-1-1-1-122-2-2-2-2111122-1-1-1-1-1-1-20-20000000001111000011000000
χ1922222222222222-12-122-12-122-1-1-1-1222222-1-100000000-1-1-1-1-1-1-1-10200200220-1-10000000000-1-100-1-1
χ2022222222222222-12-122-12-122-1-1-1-1222222-1-100000000-1-1-1-1-1-1-1-10-200-200-2-20110000000000110011
χ212222222222-2-2222-12-1-12-12-2-2-1-1-1-111-1-111222222-1-1-1-1-2-211-1-111-20-2000000000-1-111000011000000
χ222222222222-2-2222-12-1-12-12-2-2-1-1-1-111-1-11122-2-2-2-21111-2-211-1-11120200000000011-1-10000-1-1000000
χ232222222222-2-222-12-122-12-1-2-2-1-1-1-1-2-222-2-2-1-1000000001111-1-1110200-2002-20-1-10000000000-1-10011
χ242222222222-2-222-12-122-12-1-2-2-1-1-1-1-2-222-2-2-1-1000000001111-1-1110-200200-2201100000000001100-1-1
χ2522222-2-22222-2-2-22-12-1-12-12-22-1-1-1-1-1-11111-2-222-2-211112-2-1-1111120-2000000000-1-1-1-1000011000000
χ2622222-2-22222-2-2-22-12-1-12-12-22-1-1-1-1-1-11111-2-2-2-222-1-1-1-12-2-1-11111-20200000000011110000-1-1000000
χ2722222-2-22222-2-2-2-12-122-12-1-22-1-1-1-122-2-2-2-21100000000-11-1-111110200-200-220-1-1000000000011001-1
χ2822222-2-22222-2-2-2-12-122-12-1-22-1-1-1-122-2-2-2-21100000000-11-1-111110-2002002-20110000000000-1-100-11
χ2922222-2-2222-22-2-22-12-1-12-122-2-1-1-1-11111-1-1-2-222-2-21111-221111-1-1-202000000000-1-1110000-1-1000000
χ3022222-2-2222-22-2-22-12-1-12-122-2-1-1-1-11111-1-1-2-2-2-222-1-1-1-1-221111-1-120-200000000011-1-1000011000000
χ3122222-2-2222-22-2-2-12-122-12-12-2-1-1-1-1-2-2-2-22211000000001-11111-1-10200200-2-20-1-100000000001100-11
χ3222222-2-2222-22-2-2-12-122-12-12-2-1-1-1-1-2-2-2-22211000000001-11111-1-10-200-200220110000000000-1-1001-1
χ332-22-222i−2i-2-22002i−2i22-22-22-2-2002-22-2002i−2i002i−2i2-22i−2i2i2i−2i−2i00002i−2i000000000000002-200000000000000
χ342-22-222i−2i-2-22002i−2i22-22-22-2-2002-22-2002i−2i002i−2i-22−2i2i−2i−2i2i2i00002i−2i00000000000000-2200000000000000
χ352-22-222i−2i-2-22002i−2i2-1-2-1121-200-11-11−i3i3−ii3−32i−2i2-22i−2i−i−iii00−i3i3−ii3−3000000000000-11−i3i300003−3000000
χ362-22-222i−2i-2-22002i−2i2-1-2-1121-200-11-11−i3i3−ii3−32i−2i-22−2i2iii−i−i00−i3i3−ii3−30000000000001-1i3−i30000−33000000
χ372-22-222i−2i-2-22002i−2i2-1-2-1121-200-11-11i3−i3−ii−332i−2i2-22i−2i−i−iii00i3−i3−ii−33000000000000-11i3−i30000−33000000
χ382-22-222i−2i-2-22002i−2i2-1-2-1121-200-11-11i3−i3−ii−332i−2i-22−2i2iii−i−i00i3−i3−ii−330000000000001-1−i3i300003−3000000
χ392-22-22−2i2i-2-2200−2i2i22-22-22-2-2002-22-200−2i2i00−2i2i2-2−2i2i−2i−2i2i2i0000−2i2i000000000000002-200000000000000
χ402-22-22−2i2i-2-2200−2i2i22-22-22-2-2002-22-200−2i2i00−2i2i-222i−2i2i2i−2i−2i0000−2i2i00000000000000-2200000000000000
χ412-22-22−2i2i-2-2200−2i2i2-1-2-1121-200-11-11−i3i3i−i−33−2i2i2-2−2i2iii−i−i00−i3i3i−i−33000000000000-11−i3i30000−33000000
χ422-22-22−2i2i-2-2200−2i2i2-1-2-1121-200-11-11−i3i3i−i−33−2i2i-222i−2i−i−iii00−i3i3i−i−330000000000001-1i3−i300003−3000000
χ432-22-22−2i2i-2-2200−2i2i2-1-2-1121-200-11-11i3−i3i−i3−3−2i2i2-2−2i2iii−i−i00i3−i3i−i3−3000000000000-11i3−i300003−3000000
χ442-22-22−2i2i-2-2200−2i2i2-1-2-1121-200-11-11i3−i3i−i3−3−2i2i-222i−2i−i−iii00i3−i3i−i3−30000000000001-1−i3i30000−33000000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-4111122-2-222-2-20000000022-1-111-1-10000000000000000000000000000
χ4744444-4-44444-4-4-4-2-2-2-2-2-2-2-2-441111-2-222222200000000-2211-1-1-1-10000000000000000000000000000
χ4844444-4-4444-44-4-4-2-2-2-2-2-2-2-24-411112222-2-222000000002-2-1-1-1-1110000000000000000000000000000
χ4944-4-44004-4-40000444-44-4-4-40044-4-40000000000000000000000000000000000000000000000000000
χ5044-4-44004-4-400004-242-2-42-400-2-22200000000000023−2323−23000000000000000000000000000000000000
χ5144-4-44004-4-400004-242-2-42-400-2-222000000000000−2323−2323000000000000000000000000000000000000
χ5244-4-44004-4-40000-24-2-442-4200-2-2220000000000000000000000000000000000−2i32i30000000000000000
χ5344-4-44004-4-40000-24-2-442-4200-2-22200000000000000000000000000000000002i3−2i30000000000000000
χ544-44-444i−4i-4-44004i−4i-2424-4-2-4200-22-22004i−4i00−2i2i000000000000−2i2i000000000000000000000000000000
χ554-44-444i−4i-4-44004i−4i-2-22-22-222001-11-1−2i32i3−2i2i23−23−2i2i0000000000i3−i3i−i−330000000000000000000000000000
χ564-44-444i−4i-4-44004i−4i-2-22-22-222001-11-12i3−2i3−2i2i−2323−2i2i0000000000−i3i3i−i3−30000000000000000000000000000
χ574-44-44−4i4i-4-4400−4i4i-2424-4-2-4200-22-2200−4i4i002i−2i0000000000002i−2i000000000000000000000000000000
χ584-44-44−4i4i-4-4400−4i4i-2-22-22-222001-11-1−2i32i32i−2i−23232i−2i0000000000i3−i3−ii3−30000000000000000000000000000
χ594-44-44−4i4i-4-4400−4i4i-2-22-22-222001-11-12i3−2i32i−2i23−232i−2i0000000000−i3i3−ii−330000000000000000000000000000
χ604-4-44400-44-4000044-4-4-4-444004-4-440000000000000000000000000000000000000000000000000000
χ614-4-44400-44-400004-2-422-4-2400-222-2000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ624-4-44400-44-400004-2-422-4-2400-222-20000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ634-4-44400-44-40000-242-4-424-200-222-20000000000000000000000000000000000000000000000−2i32i30000
χ644-4-44400-44-40000-242-4-424-200-222-200000000000000000000000000000000000000000000002i3−2i30000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000000002022002000000-1-1-1-10000-1-100
χ666666-366-3-3-366-3-300000000-3-30000000000000000000000000000000-20-2-200-2000000111100001100
χ676666-366-3-3-3-6-6-3-300000000330000000000000000000000000000000202-200-2000000-1-1-1-100001100
χ686666-366-3-3-3-6-6-3-300000000330000000000000000000000000000000-20-2200200000011110000-1-100
χ696666-3-6-6-3-3-36-633000000003-3000000000000000000000000000000020-2200-2000000-1-11100001-100
χ706666-3-6-6-3-3-36-633000000003-30000000000000000000000000000000-202-200200000011-1-10000-1100
χ716666-3-6-6-3-3-3-663300000000-33000000000000000000000000000000020-2-2002000000-1-1110000-1100
χ726666-3-6-6-3-3-3-663300000000-330000000000000000000000000000000-202200-200000011-1-100001-100
χ7388-8-88008-8-80000-4-4-44-44440022-2-20000000000000000000000000000000000000000000000000000
χ748-8-88800-88-80000-4-44444-4-4002-2-220000000000000000000000000000000000000000000000000000
χ751212-12-12-600-6660000000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ761212-12-12-600-66600000000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ7712-1212-12-612i−12i66-600−6i6i000000000000000000000000000000000000000000000000000000000000000000
χ7812-1212-12-6−12i12i66-6006i−6i000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-1212-6006-6600000000000000000000000000000000000000000000000000000000000023−2300000000
χ8012-12-1212-6006-66000000000000000000000000000000000000000000000000000000000000−232300000000

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