Finite Group Databasebeta

← Group #13149441

Character table — Group #13149441

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order1222344666441212336666661212366612121212121212122244444444121212121212121212121212244444466661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-11-11-11-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-11-11-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11111111111-1-11111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-1-11-1111-1-1111111-1-1-1-1-1-111
χ61111111111-1-11111111111-1-11111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-11-111-1-1-1-1-1-111111111-1-1
χ71111111111-1-11111111111-1-11111-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1111-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ81111111111-1-11111111111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111
χ911111-1-11111-1-1-1111111111-11111-1-1-1-1-1-11111-1-111111111111-1-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-111-11-11
χ1011111-1-11111-1-1-1111111111-11111-1-1-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1-111-11111-1-111-1-111-1-1-1-111-1-11-11-1
χ1111111-1-11111-1-1-1111111111-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11-1-1-1-1-1111-11-111-1-1-111-1-1111111-1-1-111-1
χ1211111-1-11111-1-1-1111111111-11111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11-1-1-1-1-11111-11-1-11-1-11111-1-111-1-1111-1-11
χ1311111-1-1111-11-1-111111111-11111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-11-111-1-111111-1-111-1-111-1-11-1-11
χ1411111-1-1111-11-1-111111111-11111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-111-1-111-1111111-1-1-1-1-1-111-111-1
χ1511111-1-1111-11-1-111111111-11111111-1-1-1-1-1-1-1-1111111111111-1111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111-11-1
χ1611111-1-1111-11-1-111111111-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-11-11
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
χ1922222222222222-122-12-12-122-1-1-1-122-1-1222200000000220000-1-1-1-1-1-1-1-100202020000000000-1-1-1-100-1-1
χ2022222222222222-122-12-12-122-1-1-1-122-1-1222200000000-2-20000-1-1-1-1-1-1-1-100-20-20-2000000000011110011
χ212222222222-2-2222-1-12-12-12-2-2-1-1-1-11122-1-1112222-2-200001111-2-211-1-111-2000000-1-1110000-1-100000000
χ222222222222-2-2222-1-12-12-12-2-2-1-1-1-11122-1-111-2-2-2-2220000-1-1-1-1-2-211-1-111200000011-1-100001100000000
χ232222222222-2-222-122-12-12-1-2-2-1-1-1-1-2-2-1-122-2-2000000002200001111-1-1110020-20-20000000000-1-1-1-10011
χ242222222222-2-222-122-12-12-1-2-2-1-1-1-1-2-2-1-122-2-200000000-2-200001111-1-11100-202020000000000111100-1-1
χ2522222-2-22222-2-2-22-1-12-12-122-2-1-1-1-111-2-211-1-122-2-2220000-1-1-1-12-21111-1-1-2000000-1-11100001100000000
χ2622222-2-22222-2-2-22-1-12-12-122-2-1-1-1-111-2-211-1-1-2-222-2-2000011112-21111-1-1200000011-1-10000-1-100000000
χ2722222-2-22222-2-2-2-122-12-12-12-2-1-1-1-1-2-211-2-22200000000220000-111111-1-100-20-202000000000011-1-1001-1
χ2822222-2-22222-2-2-2-122-12-12-12-2-1-1-1-1-2-211-2-22200000000-2-20000-111111-1-1002020-20000000000-1-11100-11
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
χ3122222-2-2222-22-2-2-122-12-12-1-22-1-1-1-12211-2-2-2-2000000002200001-1-1-1111100-2020-2000000000011-1-100-11
χ3222222-2-2222-22-2-2-122-12-12-1-22-1-1-1-12211-2-2-2-200000000-2-200001-1-1-111110020-2020000000000-1-111001-1
χ332-22-2200-22-2000022-2-2-222-2002-2-220000000000002-22i−2i2i−2i22-2-20000000000000000000002i−2i00002i−2i0000
χ342-22-2200-22-2000022-2-2-222-2002-2-220000000000002-2−2i2i−2i2i22-2-2000000000000000000000−2i2i0000−2i2i0000
χ352-22-2200-22-2000022-2-2-222-2002-2-22000000000000-222i−2i−2i2i-2-2220000000000000000000002i−2i0000−2i2i0000
χ362-22-2200-22-2000022-2-2-222-2002-2-22000000000000-22−2i2i2i−2i-2-222000000000000000000000−2i2i00002i−2i0000
χ372-2-2222i−2i-2-22002i−2i222-2-2-2-22002-22-2002i−2i2i−2i002-22i−2i000000000000002i−2i0000000002-20000002i−2i00000000
χ382-2-2222i−2i-2-22002i−2i222-2-2-2-22002-22-2002i−2i2i−2i00-22−2i2i000000000000002i−2i000000000-22000000−2i2i00000000
χ392-2-2222i−2i-2-22002i−2i2-1-1-21-21200-11-11−i3i32i−2i−ii3−32-22i−2i0000003−33−300−i3i3−ii3−30000000-11−i3i30000−ii00000000
χ402-2-2222i−2i-2-22002i−2i2-1-1-21-21200-11-11−i3i32i−2i−ii3−3-22−2i2i000000−33−3300−i3i3−ii3−300000001-1i3−i30000i−i00000000
χ412-2-2222i−2i-2-22002i−2i2-1-1-21-21200-11-11i3−i32i−2i−ii−332-22i−2i000000−33−3300i3−i3−ii−330000000-11i3−i30000−ii00000000
χ422-2-2222i−2i-2-22002i−2i2-1-1-21-21200-11-11i3−i32i−2i−ii−33-22−2i2i0000003−33−300i3−i3−ii−3300000001-1−i3i30000i−i00000000
χ432-2-222−2i2i-2-2200−2i2i222-2-2-2-22002-22-200−2i2i−2i2i002-2−2i2i00000000000000−2i2i0000000002-2000000−2i2i00000000
χ442-2-222−2i2i-2-2200−2i2i222-2-2-2-22002-22-200−2i2i−2i2i00-222i−2i00000000000000−2i2i000000000-220000002i−2i00000000
χ452-2-222−2i2i-2-2200−2i2i2-1-1-21-21200-11-11−i3i3−2i2ii−i−332-2−2i2i000000−33−3300−i3i3i−i−330000000-11−i3i30000i−i00000000
χ462-2-222−2i2i-2-2200−2i2i2-1-1-21-21200-11-11−i3i3−2i2ii−i−33-222i−2i0000003−33−300−i3i3i−i−3300000001-1i3−i30000−ii00000000
χ472-2-222−2i2i-2-2200−2i2i2-1-1-21-21200-11-11i3−i3−2i2ii−i3−32-2−2i2i0000003−33−300i3−i3i−i3−30000000-11i3−i30000i−i00000000
χ482-2-222−2i2i-2-2200−2i2i2-1-1-21-21200-11-11i3−i3−2i2ii−i3−3-222i−2i000000−33−3300i3−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
χ5344-4-44004-4-4000044-444-4-4-40044-4-40000000000000000000000000000000000000000000000000000000
χ5444-4-44004-4-400004-224-2-42-400-2-22200000000000000000023−23−2323000000000000000000000000000000000
χ5544-4-44004-4-400004-224-2-42-400-2-222000000000000000000−232323−23000000000000000000000000000000000
χ5644-4-44004-4-40000-24-4-242-4200-2-22200000000000000000000000000000000000000000000000−2i32i3000000
χ5744-4-44004-4-40000-24-4-242-4200-2-222000000000000000000000000000000000000000000000002i3−2i3000000
χ584-44-4400-44-400004-22-424-2-400-222-20000000000004-40000-2-222000000000000000000000000000000000
χ594-44-4400-44-400004-22-424-2-400-222-2000000000000-44000022-2-2000000000000000000000000000000000
χ604-44-4400-44-40000-24-42-4-24200-222-200000000000000004i−4i0000000000000000000000000000000−2i2i0000
χ614-44-4400-44-40000-24-42-4-24200-222-20000000000000000−4i4i00000000000000000000000000000002i−2i0000
χ624-4-4444i−4i-4-44004i−4i-2442-42-4-200-22-2200−2i2i4i−4i00000000000000000000−2i2i000000000000000000000000000
χ634-4-4444i−4i-4-44004i−4i-2-2-22222-2001-11-1−2i32i3−2i2i−2i2i23−230000000000000000i3−i3i−i−330000000000000000000000000
χ644-4-4444i−4i-4-44004i−4i-2-2-22222-2001-11-12i3−2i3−2i2i−2i2i−23230000000000000000−i3i3i−i3−30000000000000000000000000
χ654-4-444−4i4i-4-4400−4i4i-2442-42-4-200-22-22002i−2i−4i4i000000000000000000002i−2i000000000000000000000000000
χ664-4-444−4i4i-4-4400−4i4i-2-2-22222-2001-11-1−2i32i32i−2i2i−2i−23230000000000000000i3−i3−ii3−30000000000000000000000000
χ674-4-444−4i4i-4-4400−4i4i-2-2-22222-2001-11-12i3−2i32i−2i2i−2i23−230000000000000000−i3i3−ii−330000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-3000000000000000000220000000000000002020200000-1-1-1-1000000-1-100
χ696666-366-3-3-366-3-300000000-3-3000000000000000000-2-2000000000000000-20-20-20000011110000001100
χ706666-366-3-3-3-6-6-3-300000000330000000000000000002200000000000000020-20-200000-1-1-1-10000001100
χ716666-366-3-3-3-6-6-3-30000000033000000000000000000-2-2000000000000000-20202000001111000000-1-100
χ726666-3-6-6-3-3-36-63300000000-3300000000000000000022000000000000000-20-2020000011-1-10000001-100
χ736666-3-6-6-3-3-36-63300000000-33000000000000000000-2-20000000000000002020-200000-1-111000000-1100
χ746666-3-6-6-3-3-3-6633000000003-300000000000000000022000000000000000-2020-20000011-1-1000000-1100
χ756666-3-6-6-3-3-3-6633000000003-3000000000000000000-2-200000000000000020-20200000-1-1110000001-100
χ7688-8-88008-8-80000-4-44-4-44440022-2-20000000000000000000000000000000000000000000000000000000
χ778-88-8800-88-80000-4-4444-4-44002-2-220000000000000000000000000000000000000000000000000000000
χ781212-12-12-600-66600000000000000000000000000000000000000000000000000000000000−2i32i3000000000000
χ791212-12-12-600-666000000000000000000000000000000000000000000000000000000000002i3−2i3000000000000
χ8012-1212-12-6006-66000000000000000000000000000000004i−4i000000000000000000000000000−2i2i0000000000
χ8112-1212-12-6006-6600000000000000000000000000000000−4i4i0000000000000000000000000002i−2i0000000000
χ8212-12-1212-612i−12i66-600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-6−12i12i66-6006i−6i000000000000000000000000000000000000000000000000000000000000000000000

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