Finite Group Databasebeta

← Group #13149493

Character table — Group #13149493

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order12223446664412123366666612123666121212121212121222444444441212121212121212121212122444444661212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-1-111-1-1-1-111-1-1-1-1-1-11-1-11
χ3111111111111111111111111111111111111-1-1111111-1-1111111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-11-11-1-11111-1-1-1-1-1-1-1-1-111-1
χ51111111111-1-11111111111-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-11-111111111-1-111-1-1-1-1-1-1
χ61111111111-1-11111111111-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1111-1-1-1-11111-1-111-111-1
χ71111111111-1-11111111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111-1-11111
χ81111111111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-11111-1-111-1-1111-1-11
χ911111-1-11111-1-1-1111111111-11111-1-1-1-111-1-11111-1-111111111-11-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-1111-11-1
χ1011111-1-11111-1-1-1111111111-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1111-11-111-11111-1-1-1-11111-1-111-1-1
χ1111111-1-11111-1-1-1111111111-11111-1-1-1-111-1-1-1-111-1-111-1-11111-11-1-1-1-111-11111-1-1-1-111-1-111-1-1-1-111-11-11
χ1211111-1-11111-1-1-1111111111-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-11-1-1-1-111-11-11-111-1-1-1-111111111-1-1-1-111
χ1311111-1-1111-11-1-111111111-111111-1-1-1-1-1-111111111-1-11111111-111-1-1-1-1-11-1-11-1-111-1-111-1-111-1-1-1-1-11-11
χ1411111-1-1111-11-1-111111111-111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-111-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-111
χ1511111-1-1111-11-1-111111111-111111-1-1-1-1-1-111-1-11111-1-1-1-111111-111-1-1-1-11-111-1-11-1-111-1-11111-1-1-1-11-11-1
χ1611111-1-1111-11-1-111111111-111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-111-1-1-1-11-1-1111-1-1-1-1-11111-1-1111111-1-1
χ17222222222222222-1-12-12-1222-1-1-1-122-1-1222222000000000000-1-1-1-1-1-1-1-12202000-1-10000-1-1000000-100-1
χ18222222222222222-1-12-12-1222-1-1-1-122-1-12222-2-2000000000000-1-1-1-1-1-1-1-1-2-20-2000110000110000001001
χ1922222222222222-122-12-12-122-1-1-1-1-1-122-1-1-1-10022222200-1-1-1-122-1-1-1-1-1-1000002000000000-1-1-1-1-1-10000
χ2022222222222222-122-12-12-122-1-1-1-1-1-122-1-1-1-100-2-2-2-2-2-200111122-1-1-1-1-1-100000-20000000001111110000
χ212222222222-2-2222-1-12-12-12-2-2-1-1-1-122-1-1-2-2-2-2220000000000001111-1-111-2-202000-1-10000-1-10000001001
χ222222222222-2-2222-1-12-12-12-2-2-1-1-1-122-1-1-2-2-2-2-2-20000000000001111-1-111220-200011000011000000-100-1
χ232222222222-2-222-122-12-12-1-2-2-1-1-1-1-1-12211110022-2-2-2-200-1-1-1-1-2-211-1-11100000200000000011-1-1110000
χ242222222222-2-222-122-12-12-1-2-2-1-1-1-1-1-122111100-2-22222001111-2-211-1-11100000-2000000000-1-111-1-10000
χ2522222-2-22222-2-2-22-1-12-12-122-2-1-1-1-1-2-21122-2-2220000000000001-11111-1-12-20-2000-1-1000011000000-1001
χ2622222-2-22222-2-2-22-1-12-12-122-2-1-1-1-1-2-21122-2-2-2-20000000000001-11111-1-1-2202000110000-1-1000000100-1
χ2722222-2-22222-2-2-2-122-12-12-12-2-1-1-1-111-2-2-1-1110022-2-22200-1-1-1-1-221111-1-100000-20000000001111-1-10000
χ2822222-2-22222-2-2-2-122-12-12-12-2-1-1-1-111-2-2-1-11100-2-222-2-2001111-221111-1-1000002000000000-1-1-1-1110000
χ2922222-2-2222-22-2-22-1-12-12-12-22-1-1-1-1-2-211-2-22222000000000000-11-1-11111-220-2000-1-1000011000000100-1
χ3022222-2-2222-22-2-22-1-12-12-12-22-1-1-1-1-2-211-2-222-2-2000000000000-11-1-111112-202000110000-1-1000000-1001
χ3122222-2-2222-22-2-2-122-12-12-1-22-1-1-1-111-2-211-1-1002222-2-200-1-1-1-12-2-1-1111100000-2000000000-1-111110000
χ3222222-2-2222-22-2-2-122-12-12-1-22-1-1-1-111-2-211-1-100-2-2-2-2220011112-2-1-1111100000200000000011-1-1-1-10000
χ332-22-2200-22-2000022-2-2-222-2002-2-22000000002-22i−2i00002i−2i2i2i−2i−2i0000000000000002-2002i−2i000000000000
χ342-22-2200-22-2000022-2-2-222-2002-2-22000000002-2−2i2i0000−2i2i−2i−2i2i2i0000000000000002-200−2i2i000000000000
χ352-22-2200-22-2000022-2-2-222-2002-2-2200000000-222i−2i0000−2i2i2i2i−2i−2i000000000000000-2200−2i2i000000000000
χ362-22-2200-22-2000022-2-2-222-2002-2-2200000000-22−2i2i00002i−2i−2i−2i2i2i000000000000000-22002i−2i000000000000
χ372-2-2222i−2i-2-22002i−2i222-2-2-2-22002-22-22i−2i2i−2i000000002i−2i2-200000000002i−2i000000000000000002i−2i002-20000
χ382-2-2222i−2i-2-22002i−2i222-2-2-2-22002-22-22i−2i2i−2i00000000−2i2i-2200000000002i−2i00000000000000000−2i2i00-220000
χ392-2-2222i−2i-2-22002i−2i-1221-21-2-100-11-11−ii2i−2i3−3−i3i300002i−2i2-2003−33−300−i3i3−ii3−3000000000000000−ii−i3i3-110000
χ402-2-2222i−2i-2-22002i−2i-1221-21-2-100-11-11−ii2i−2i3−3−i3i30000−2i2i-2200−33−3300−i3i3−ii3−3000000000000000i−ii3−i31-10000
χ412-2-2222i−2i-2-22002i−2i-1221-21-2-100-11-11−ii2i−2i−33i3−i300002i−2i2-200−33−3300i3−i3−ii−33000000000000000−iii3−i3-110000
χ422-2-2222i−2i-2-22002i−2i-1221-21-2-100-11-11−ii2i−2i−33i3−i30000−2i2i-22003−33−300i3−i3−ii−33000000000000000i−i−i3i31-10000
χ432-2-222−2i2i-2-2200−2i2i222-2-2-2-22002-22-2−2i2i−2i2i000000002i−2i-220000000000−2i2i000000000000000002i−2i00-220000
χ442-2-222−2i2i-2-2200−2i2i222-2-2-2-22002-22-2−2i2i−2i2i00000000−2i2i2-20000000000−2i2i00000000000000000−2i2i002-20000
χ452-2-222−2i2i-2-2200−2i2i-1221-21-2-100-11-11i−i−2i2i3−3i3−i300002i−2i-2200−33−3300i3−i3i−i3−3000000000000000−ii−i3i31-10000
χ462-2-222−2i2i-2-2200−2i2i-1221-21-2-100-11-11i−i−2i2i3−3i3−i30000−2i2i2-2003−33−300i3−i3i−i3−3000000000000000i−ii3−i3-110000
χ472-2-222−2i2i-2-2200−2i2i-1221-21-2-100-11-11i−i−2i2i−33−i3i300002i−2i-22003−33−300−i3i3i−i−33000000000000000−iii3−i31-10000
χ482-2-222−2i2i-2-2200−2i2i-1221-21-2-100-11-11i−i−2i2i−33−i3i30000−2i2i2-200−33−3300−i3i3i−i−33000000000000000i−i−i3i3-110000
χ4944444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000000000-2-21111110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-41111-2-2-2-222220000000000000022-1-111-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-411112222-2-222000000000000002-2-1-1-1-1110000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-441111222222-2-200000000000000-2211-1-1-1-10000000000000000000000000
χ5344-4-44004-4-4000044-444-4-4-40044-4-40000000000000000000000000000000000000000000000000000000
χ5444-4-44004-4-400004-224-2-42-400-2-222000000000000000000000000000000000000000000023−230000000000
χ5544-4-44004-4-400004-224-2-42-400-2-2220000000000000000000000000000000000000000000−23230000000000
χ5644-4-44004-4-40000-24-4-242-4200-2-222000000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ5744-4-44004-4-40000-24-4-242-4200-2-2220000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ584-44-4400-44-400004-22-424-2-400-222-2000000004-4000000000000000000000000000-220000000000000000
χ594-44-4400-44-400004-22-424-2-400-222-200000000-440000000000000000000000000002-20000000000000000
χ604-44-4400-44-40000-24-42-4-24200-222-200000000004i−4i000000−2i−2i2i2i000000000000000000000000000000000
χ614-44-4400-44-40000-24-42-4-24200-222-20000000000−4i4i0000002i2i−2i−2i000000000000000000000000000000000
χ624-4-4444i−4i-4-44004i−4i4-2-2-42-42400-22-224i−4i−2i2i0000000000000000000000−2i2i000000000000000000000000000
χ634-4-4444i−4i-4-44004i−4i-2-2-22222-2001-11-1−2i2i−2i2i23−23−2i32i30000000000000000i3−i3i−i−330000000000000000000000000
χ644-4-4444i−4i-4-44004i−4i-2-2-22222-2001-11-1−2i2i−2i2i−23232i3−2i30000000000000000−i3i3i−i3−30000000000000000000000000
χ654-4-444−4i4i-4-4400−4i4i4-2-2-42-42400-22-22−4i4i2i−2i00000000000000000000002i−2i000000000000000000000000000
χ664-4-444−4i4i-4-4400−4i4i-2-2-22222-2001-11-12i−2i2i−2i23−232i3−2i30000000000000000−i3i3−ii−330000000000000000000000000
χ674-4-444−4i4i-4-4400−4i4i-2-2-22222-2001-11-12i−2i2i−2i−2323−2i32i30000000000000000i3−i3−ii3−30000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-30000000000000000000022000000000000002020200-1-1-1-1000000000-1-10
χ696666-366-3-3-366-3-300000000-3-300000000000000000000-2-200000000000000-20-20-2001111000000000110
χ706666-366-3-3-3-6-6-3-3000000003300000000000000000000220000000000000020-20-200-1-1-1-1000000000110
χ716666-366-3-3-3-6-6-3-3000000003300000000000000000000-2-200000000000000-20202001111000000000-1-10
χ726666-3-6-6-3-3-36-63300000000-33000000000000000000002200000000000000-20-2020011-1-10000000001-10
χ736666-3-6-6-3-3-36-63300000000-3300000000000000000000-2-2000000000000002020-200-1-111000000000-110
χ746666-3-6-6-3-3-3-6633000000003-3000000000000000000002200000000000000-2020-20011-1-1000000000-110
χ756666-3-6-6-3-3-3-6633000000003-300000000000000000000-2-20000000000000020-20200-1-1110000000001-10
χ7688-8-88008-8-80000-4-44-4-44440022-2-20000000000000000000000000000000000000000000000000000000
χ778-88-8800-88-80000-4-4444-4-44002-2-220000000000000000000000000000000000000000000000000000000
χ781212-12-12-600-666000000000000000000000000000000000000000000000000000000000−2i32i300000000000000
χ791212-12-12-600-6660000000000000000000000000000000000000000000000000000000002i3−2i300000000000000
χ8012-1212-12-6006-6600000000000000000000000000000000004i−4i00000000000000000000000−2i2i000000000000
χ8112-1212-12-6006-660000000000000000000000000000000000−4i4i000000000000000000000002i−2i000000000000
χ8212-12-1212-612i−12i66-600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-6−12i12i66-6006i−6i000000000000000000000000000000000000000000000000000000000000000000000

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