Finite Group Databasebeta

← Group #13148548

Character table — Group #13148548

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order122234466624121233666666612366666121212121212222244444466666661212121212244444466661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-111-1-11-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111-1-11111111111-1-11-1-111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-11-11-1-11-1-111111111-1-1-1-1-1-111
χ61111111111-1-11111111111-1-11-1-111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-111-1-11-11-1-11-11111-1-1-1-111-1-11111-1-1
χ71111111111-1-11111111111-1-11-1-111111-1-111-1-111-1-111111111-1-1-1-111-1-111-1-11-1-111-1-11111-1-11111-1-1-1-1
χ81111111111-1-11111111111-1-11-1-111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-11111-1-111111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-1111-11-1
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1111-1-1-11111111-1-1-1-1-1-1-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-11-1-1-111111-1-1-1-1111111-1-11-1-11
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-111-1
χ1311111-1-1111-11-1-111111111-111-1-1111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1111-1111-1-11111-1-111-1-111-1-1-111-1
χ1411111-1-1111-11-1-111111111-111-1-1111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111-11-1-1111-1-11111-1-1-1-111111-1-11
χ1511111-1-1111-11-1-111111111-111-1-1111-1-111-1-1-1-1111111111111-1-1-11-1-111-1-11-1-1-11-1-1-1-1-1-11111-1-111-11-11
χ1611111-1-1111-11-1-111111111-111-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-11-1-11111-11-11-111-1-111-1-111-1-1-1-11-11-1
χ17222222222222222-1-122-1-1222-1-1-1-1-1-1-1-1-1-1222222220000-1-1-1-12-1-12-1-1-1-1000020000-1-10000-1-1-1-1000000
χ18222222222222222-1-122-1-1222-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2000011112-1-12-1-1-1-10000-200001100001111000000
χ1922222222222222-122-1-122-122-122-1-1-12222-1-100000000220000-1-1-1-1-1-1-1-12002002-1-10000000000-1-100-1-1
χ2022222222222222-122-1-122-122-122-1-1-12222-1-100000000-2-20000-1-1-1-1-1-1-1-1-200-200-2110000000000110011
χ212222222222-2-2222-1-122-1-12-2-2-111-1-1-1-1-1112222-2-22200001111-211-2-1-1110000-20000-1-10000-1-111000000
χ222222222222-2-2222-1-122-1-12-2-2-111-1-1-1-1-11122-2-222-2-20000-1-1-1-1-211-2-1-11100002000011000011-1-1000000
χ232222222222-2-222-122-1-122-1-2-2-1-2-2-1-1-122-2-2-1-1000000002200001111-1-111200-200-2-1-10000000000-1-10011
χ242222222222-2-222-122-1-122-1-2-2-1-2-2-1-1-122-2-2-1-100000000-2-200001111-1-111-20020021100000000001100-1-1
χ2522222-2-22222-2-2-22-1-122-1-122-2-1-1-1-1-1-11111-2-22222-2-20000-1-1-1-12-1-1-211110000-20000-1-100001111000000
χ2622222-2-22222-2-2-22-1-122-1-122-2-1-1-1-1-1-11111-2-2-2-2-2-222000011112-1-1-21111000020000110000-1-1-1-1000000
χ2722222-2-22222-2-2-2-122-1-122-12-2-122-1-1-1-2-2-2-21100000000220000-1-1-111111-200200-2110000000000-1-100-11
χ2822222-2-22222-2-2-2-122-1-122-12-2-122-1-1-1-2-2-2-21100000000-2-20000-1-1-111111200-2002-1-1000000000011001-1
χ2922222-2-2222-22-2-22-1-122-1-12-22-111-1-1-111-1-1-2-222-2-2-2-200001111-211211-1-1000020000-1-1000011-1-1000000
χ3022222-2-2222-22-2-22-1-122-1-12-22-111-1-1-111-1-1-2-2-2-222220000-1-1-1-1-211211-1-10000-20000110000-1-111000000
χ3122222-2-2222-22-2-2-122-1-122-1-22-1-2-2-1-1-1-2-2221100000000220000111-111-1-1-200-2002110000000000-1-1001-1
χ3222222-2-2222-22-2-2-122-1-122-1-22-1-2-2-1-1-1-2-2221100000000-2-20000111-111-1-1200200-2-1-100000000001100-11
χ3322-2-22002-2-2000022-22-22-2-200200-22-2000000002-2002i−2i2i−2i22-2-20000000000000000000002i−2i00002i−2i0000
χ3422-2-22002-2-2000022-22-22-2-200200-22-2000000002-200−2i2i−2i2i22-2-2000000000000000000000−2i2i0000−2i2i0000
χ3522-2-22002-2-2000022-22-22-2-200200-22-200000000-22002i−2i−2i2i-2-2220000000000000000000002i−2i0000−2i2i0000
χ3622-2-22002-2-2000022-22-22-2-200200-22-200000000-2200−2i2i2i−2i-2-222000000000000000000000−2i2i00002i−2i0000
χ372-22-222i−2i-2-22002i−2i222-22-2-2-2002002-2-22i−2i002i−2i2-2002i−2i0000000000002i−2i000000000002-200002i−2i00000000
χ382-22-222i−2i-2-22002i−2i222-22-2-2-2002002-2-22i−2i002i−2i-2200−2i2i0000000000002i−2i00000000000-220000−2i2i00000000
χ392-22-222i−2i-2-22002i−2i2-1-1-2211-200-1−i3i3-111−ii3−32i−2i2-2002i−2i0000−i3i3−i3i30−i3i30−ii3−3000000000-110000−ii3−3000000
χ402-22-222i−2i-2-22002i−2i2-1-1-2211-200-1−i3i3-111−ii3−32i−2i-2200−2i2i0000i3−i3i3−i30−i3i30−ii3−30000000001-10000i−i−33000000
χ412-22-222i−2i-2-22002i−2i2-1-1-2211-200-1i3−i3-111−ii−332i−2i2-2002i−2i0000i3−i3i3−i30i3−i30−ii−33000000000-110000−ii−33000000
χ422-22-222i−2i-2-22002i−2i2-1-1-2211-200-1i3−i3-111−ii−332i−2i-2200−2i2i0000−i3i3−i3i30i3−i30−ii−330000000001-10000i−i3−3000000
χ432-22-22−2i2i-2-2200−2i2i222-22-2-2-2002002-2-2−2i2i00−2i2i2-200−2i2i000000000000−2i2i000000000002-20000−2i2i00000000
χ442-22-22−2i2i-2-2200−2i2i222-22-2-2-2002002-2-2−2i2i00−2i2i-22002i−2i000000000000−2i2i00000000000-2200002i−2i00000000
χ452-22-22−2i2i-2-2200−2i2i2-1-1-2211-200-1−i3i3-111i−i−33−2i2i2-200−2i2i0000−i3i3−i3i30−i3i30i−i−33000000000-110000i−i−33000000
χ462-22-22−2i2i-2-2200−2i2i2-1-1-2211-200-1−i3i3-111i−i−33−2i2i-22002i−2i0000i3−i3i3−i30−i3i30i−i−330000000001-10000−ii3−3000000
χ472-22-22−2i2i-2-2200−2i2i2-1-1-2211-200-1i3−i3-111i−i3−3−2i2i2-200−2i2i0000i3−i3i3−i30i3−i30i−i3−3000000000-110000i−i3−3000000
χ482-22-22−2i2i-2-2200−2i2i2-1-1-2211-200-1i3−i3-111i−i3−3−2i2i-22002i−2i0000−i3i3−i3i30i3−i30i−i3−30000000001-10000−ii−33000000
χ4944444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2-2-2-2-200000000000000-211-211110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-4122111-2-222-2-2000000000000002-1-1211-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-211122222200000000000000-2112-1-1-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-4412211122-2-222000000000000002-1-1-2-1-1110000000000000000000000000
χ5344-4-44004-4-400004-224-4-22-400-2002-22000000004-4000000-2-222000000000000000000000000000000000
χ5444-4-44004-4-400004-224-4-22-400-2002-2200000000-4400000022-2-2000000000000000000000000000000000
χ5544-4-44004-4-40000-24-4-224-4200-2002-22000000000000004i−4i0000000000000000000000000000000−2i2i0000
χ5644-4-44004-4-40000-24-4-224-4200-2002-2200000000000000−4i4i00000000000000000000000000000002i−2i0000
χ574-44-444i−4i-4-44004i−4i-2442-2-4-4200-200-2224i−4i00−2i2i000000000000000000−2i2i000000000000000000000000000
χ584-44-444i−4i-4-44004i−4i-2-2-22-2222001−2i32i31-1-1−2i2i23−23−2i2i000000000000000i3−i30i−i−330000000000000000000000000
χ594-44-444i−4i-4-44004i−4i-2-2-22-22220012i3−2i31-1-1−2i2i−2323−2i2i000000000000000−i3i30i−i3−30000000000000000000000000
χ604-44-44−4i4i-4-4400−4i4i-2442-2-4-4200-200-222−4i4i002i−2i0000000000000000002i−2i000000000000000000000000000
χ614-44-44−4i4i-4-4400−4i4i-2-2-22-2222001−2i32i31-1-12i−2i−23232i−2i000000000000000i3−i30−ii3−30000000000000000000000000
χ624-44-44−4i4i-4-4400−4i4i-2-2-22-22220012i3−2i31-1-12i−2i23−232i−2i000000000000000−i3i30−ii−330000000000000000000000000
χ634-4-44400-44-4000044-4-4-4-44400400-4-4400000000000000000000000000000000000000000000000000000
χ644-4-44400-44-400004-22-4-42-2400-20022-20000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ654-4-44400-44-400004-22-4-42-2400-20022-200000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ664-4-44400-44-40000-24-422-44-200-20022-200000000000000000000000000000000000−2i32i30000000000000000
χ674-4-44400-44-40000-24-422-44-200-20022-2000000000000000000000000000000000002i3−2i30000000000000000
χ686666-366-3-3-366-3-300000000-3-3000000000000000000220000000000000002200200000-1-1-1-1000000-1-100
χ696666-366-3-3-366-3-300000000-3-3000000000000000000-2-2000000000000000-2-200-20000011110000001100
χ706666-366-3-3-3-6-6-3-30000000033000000000000000000220000000000000002-200-200000-1-1-1-10000001100
χ716666-366-3-3-3-6-6-3-30000000033000000000000000000-2-2000000000000000-22002000001111000000-1-100
χ726666-3-6-6-3-3-36-63300000000-3300000000000000000022000000000000000-2-20020000011-1-1000000-1100
χ736666-3-6-6-3-3-36-63300000000-33000000000000000000-2-20000000000000002200-200000-1-1110000001-100
χ746666-3-6-6-3-3-3-6633000000003-300000000000000000022000000000000000-2200-20000011-1-10000001-100
χ756666-3-6-6-3-3-3-6633000000003-3000000000000000000-2-20000000000000002-200200000-1-111000000-1100
χ7688-8-88008-8-80000-4-44-44-44400200-22-200000000000000000000000000000000000000000000000000000
χ778-8-88800-88-80000-4-44444-4-400200-2-2200000000000000000000000000000000000000000000000000000
χ781212-12-12-600-666000000000000000000000000000000004i−4i000000000000000000000000000−2i2i0000000000
χ791212-12-12-600-66600000000000000000000000000000000−4i4i0000000000000000000000000002i−2i0000000000
χ8012-1212-12-612i−12i66-600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6−12i12i66-6006i−6i000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-6006-660000000000000000000000000000000000000000000000000000000000023−23000000000000
χ8312-12-1212-6006-6600000000000000000000000000000000000000000000000000000000000−2323000000000000

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