Finite Group Databasebeta

← Group #13149527

Character table — Group #13149527

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order12223446664412123366666612123666121212121212121222444444441212121212121212121212122224444666612121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-11-11-11-1-1-1-1-11111-1-1-1-1-1-11-11-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-11-11-1-1-1-1-1-1-1-1-1-11111-11-11
χ51111111111-1-11111111111-1-11111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111-1-1111111-1-1-1-1-11-11
χ61111111111-1-11111111111-1-11111-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-11-1-111-111-1-1-1-1-1-11111111-11-1
χ71111111111-1-11111111111-1-11111-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-11-1-111-1-1-1-1111111-1-11111-1-1-1-1
χ81111111111-1-11111111111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ911111-1-11111-1-1-1111111111-11111-1-1-1-1-1-1111111-1-1111111111-1-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ1011111-1-11111-1-1-1111111111-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-111-11111-1-111-1-111-1-1-1-111-1-111-1-1
χ1111111-1-11111-1-1-1111111111-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1111-11-111-1-1-111-1-1111111-1-1-111-1
χ1211111-1-11111-1-1-1111111111-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11-1-1-1-1-11111-11-1-11-1-11111-1-111-1-1111-1-11
χ1311111-1-1111-11-1-111111111-11111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-111-1-11-111111-1-111-1-111-1-11-1-11
χ1411111-1-1111-11-1-111111111-11111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-11-111-11-1111111-1-1-1-1-1-111-111-1
χ1511111-1-1111-11-1-111111111-11111111-1-1-1-1-1-1-1-1111111111111-1111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111-1-1111-11-1-111111111-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111
χ17222222222222222-1-12-12-1222-1-1-1-1-1-122-1-1-1-12222220000-1-1-1-122-1-1-1-1-1-12000000-1-1-1-10000-1-100000000
χ18222222222222222-1-12-12-1222-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-20000111122-1-1-1-1-1-1-2000000111100001100000000
χ1922222222222222-122-12-12-122-1-1-1-122-1-1222200000000220000-1-1-1-1-1-1-1-100202020000000000-1-1-1-10-10-1
χ2022222222222222-122-12-12-122-1-1-1-122-1-1222200000000-2-20000-1-1-1-1-1-1-1-100-20-20-2000000000011110101
χ212222222222-2-2222-1-12-12-12-2-2-1-1-1-11122-1-11122-2-22200001111-2-211-1-111-2000000-1-1110000-1-100000000
χ222222222222-2-2222-1-12-12-12-2-2-1-1-1-11122-1-111-2-222-2-20000-1-1-1-1-2-211-1-111200000011-1-100001100000000
χ232222222222-2-222-122-12-12-1-2-2-1-1-1-1-2-2-1-122-2-2000000002200001111-1-11100-2020-20000000000-1-1-1-10101
χ242222222222-2-222-122-12-12-1-2-2-1-1-1-1-2-2-1-122-2-200000000-2-200001111-1-1110020-202000000000011110-10-1
χ2522222-2-22222-2-2-22-1-12-12-122-2-1-1-1-111-2-211-1-12222-2-20000-1-1-1-12-21111-1-1-2000000-1-11100001100000000
χ2622222-2-22222-2-2-22-1-12-12-122-2-1-1-1-111-2-211-1-1-2-2-2-222000011112-21111-1-1200000011-1-10000-1-100000000
χ2722222-2-22222-2-2-2-122-12-12-12-2-1-1-1-1-2-211-2-22200000000220000-111111-1-100-20-202000000000011-1-1010-1
χ2822222-2-22222-2-2-2-122-12-12-12-2-1-1-1-1-2-211-2-22200000000-2-20000-111111-1-1002020-20000000000-1-1110-101
χ2922222-2-2222-22-2-22-1-12-12-12-22-1-1-1-1-1-1-2-2111122-2-2-2-200001111-22-1-111112000000-1-1-1-100001100000000
χ3022222-2-2222-22-2-22-1-12-12-12-22-1-1-1-1-1-1-2-21111-2-222220000-1-1-1-1-22-1-11111-200000011110000-1-100000000
χ3122222-2-2222-22-2-2-122-12-12-1-22-1-1-1-12211-2-2-2-2000000002200001-1-1-111110020-20-2000000000011-1-10-101
χ3222222-2-2222-22-2-2-122-12-12-1-22-1-1-1-12211-2-2-2-200000000-2-200001-1-1-1111100-202020000000000-1-111010-1
χ3322-2-22002-2-2000022-22-2-22-2002-2-2200000000002-2002i−2i2i−2i22-2-20000000000000000000002i−2i00002i−2i0000
χ3422-2-22002-2-2000022-22-2-22-2002-2-2200000000002-200−2i2i−2i2i22-2-2000000000000000000000−2i2i0000−2i2i0000
χ3522-2-22002-2-2000022-22-2-22-2002-2-220000000000-22002i−2i−2i2i-2-2220000000000000000000002i−2i0000−2i2i0000
χ3622-2-22002-2-2000022-22-2-22-2002-2-220000000000-2200−2i2i2i−2i-2-222000000000000000000000−2i2i00002i−2i0000
χ372-22-222i−2i-22-2002i−2i222-2-22-2-2002-22-2002i−2i2i−2i002-2002i−2i0000000000002i−2i0000000002-20000002i−2i00000000
χ382-22-222i−2i-22-2002i−2i222-2-22-2-2002-22-2002i−2i2i−2i00-2200−2i2i0000000000002i−2i000000000-22000000−2i2i00000000
χ392-22-222i−2i-22-2002i−2i2-1-1-2121-200-11-11−i3i32i−2i−ii3−32-2002i−2i00003−33−300−i3i3−ii3−30000000-11−i3i30000−ii00000000
χ402-22-222i−2i-22-2002i−2i2-1-1-2121-200-11-11−i3i32i−2i−ii3−3-2200−2i2i0000−33−3300−i3i3−ii3−300000001-1i3−i30000i−i00000000
χ412-22-222i−2i-22-2002i−2i2-1-1-2121-200-11-11i3−i32i−2i−ii−332-2002i−2i0000−33−3300i3−i3−ii−330000000-11i3−i30000−ii00000000
χ422-22-222i−2i-22-2002i−2i2-1-1-2121-200-11-11i3−i32i−2i−ii−33-2200−2i2i00003−33−300i3−i3−ii−3300000001-1−i3i30000i−i00000000
χ432-22-22−2i2i-22-200−2i2i222-2-22-2-2002-22-200−2i2i−2i2i002-200−2i2i000000000000−2i2i0000000002-2000000−2i2i00000000
χ442-22-22−2i2i-22-200−2i2i222-2-22-2-2002-22-200−2i2i−2i2i00-22002i−2i000000000000−2i2i000000000-220000002i−2i00000000
χ452-22-22−2i2i-22-200−2i2i2-1-1-2121-200-11-11−i3i3−2i2ii−i−332-200−2i2i0000−33−3300−i3i3i−i−330000000-11−i3i30000i−i00000000
χ462-22-22−2i2i-22-200−2i2i2-1-1-2121-200-11-11−i3i3−2i2ii−i−33-22002i−2i00003−33−300−i3i3i−i−3300000001-1i3−i30000−ii00000000
χ472-22-22−2i2i-22-200−2i2i2-1-1-2121-200-11-11i3−i3−2i2ii−i3−32-200−2i2i00003−33−300i3−i3i−i3−30000000-11i3−i30000i−i00000000
χ482-22-22−2i2i-22-200−2i2i2-1-1-2121-200-11-11i3−i3−2i2ii−i3−3-22002i−2i0000−33−3300i3−i3i−i3−300000001-1−i3i30000−ii00000000
χ4944444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000000000-2-21111110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-4111122-2-2-2-2220000000000000022-1-111-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41111222222-2-200000000000000-22-1-1-1-1110000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-441111-2-2222222000000000000002-211-1-1-1-10000000000000000000000000
χ5344-4-44004-4-400004-2242-4-2-400-222-200000000004-4000000-2-222000000000000000000000000000000000
χ5444-4-44004-4-400004-2242-4-2-400-222-20000000000-4400000022-2-2000000000000000000000000000000000
χ5544-4-44004-4-40000-24-4-2-424200-222-200000000000000004i−4i0000000000000000000000000000000−2i2i0000
χ5644-4-44004-4-40000-24-4-2-424200-222-20000000000000000−4i4i00000000000000000000000000000002i−2i0000
χ574-44-444i−4i-44-4004i−4i-2442-4-2-4200-22-2200−2i2i4i−4i00000000000000000000−2i2i000000000000000000000000000
χ584-44-444i−4i-44-4004i−4i-2-2-222-222001-11-1−2i32i3−2i2i−2i2i23−230000000000000000i3−i3i−i−330000000000000000000000000
χ594-44-444i−4i-44-4004i−4i-2-2-222-222001-11-12i3−2i3−2i2i−2i2i−23230000000000000000−i3i3i−i3−30000000000000000000000000
χ604-44-44−4i4i-44-400−4i4i-2442-4-2-4200-22-22002i−2i−4i4i000000000000000000002i−2i000000000000000000000000000
χ614-44-44−4i4i-44-400−4i4i-2-2-222-222001-11-1−2i32i32i−2i2i−2i−23230000000000000000i3−i3−ii3−30000000000000000000000000
χ624-44-44−4i4i-44-400−4i4i-2-2-222-222001-11-12i3−2i32i−2i2i−2i23−230000000000000000−i3i3−ii−330000000000000000000000000
χ634-4-44400-4-44000044-4-44-4-440044-4-40000000000000000000000000000000000000000000000000000000
χ644-4-44400-4-4400004-22-4-2-42400-2-22200000000000000000023−23−2323000000000000000000000000000000000
χ654-4-44400-4-4400004-22-4-2-42400-2-222000000000000000000−232323−23000000000000000000000000000000000
χ664-4-44400-4-440000-24-4242-4-200-2-2220000000000000000000000000000000000000000000000023−23000000
χ674-4-44400-4-440000-24-4242-4-200-2-22200000000000000000000000000000000000000000000000−2323000000
χ686666-366-3-3-366-3-300000000-3-3000000000000000000220000000000000002020200000-1-1-1-1000000-10-10
χ696666-366-3-3-366-3-300000000-3-3000000000000000000-2-2000000000000000-20-20-20000011110000001010
χ706666-366-3-3-3-6-6-3-3000000003300000000000000000022000000000000000-2020-200000-1-1-1-10000001010
χ716666-366-3-3-3-6-6-3-30000000033000000000000000000-2-200000000000000020-202000001111000000-10-10
χ726666-3-6-6-3-3-36-63300000000-3300000000000000000022000000000000000-20-2020000011-1-100000010-10
χ736666-3-6-6-3-3-36-63300000000-33000000000000000000-2-20000000000000002020-200000-1-111000000-1010
χ746666-3-6-6-3-3-3-6633000000003-30000000000000000002200000000000000020-20-20000011-1-1000000-1010
χ756666-3-6-6-3-3-3-6633000000003-3000000000000000000-2-2000000000000000-2020200000-1-11100000010-10
χ7688-8-88008-8-80000-4-44-444-44002-2-220000000000000000000000000000000000000000000000000000000
χ778-8-88800-8-880000-4-444-444-40022-2-20000000000000000000000000000000000000000000000000000000
χ781212-12-12-600-666000000000000000000000000000000004i−4i000000000000000000000000000−2i2i0000000000
χ791212-12-12-600-66600000000000000000000000000000000−4i4i0000000000000000000000000002i−2i0000000000
χ8012-1212-12-612i−12i6-6600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6−12i12i6-66006i−6i000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-60066-60000000000000000000000000000000000000000000000000000000000023−23000000000000
χ8312-12-1212-60066-600000000000000000000000000000000000000000000000000000000000−2323000000000000

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