Finite Group Databasebeta

← Group #13148458

Character table — Group #13148458

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order122234466624121233666666612366666121212121212444444444412121212666121212121222222446666661212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-111-1-11-111-1-1-1-111-1-1-1-1-1-11-11-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-111-11-1-1-1-111-1-1-1-111-1-1-11-11
χ51111111111-1-11111111111-1-11-1-1111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-11-1-1111-1-1-1-11111-1-111-11-11
χ61111111111-1-11111111111-1-11-1-1111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-1-1-1-111-1-11111111-11-1
χ71111111111-1-11111111111-1-11-1-1111-1-11111-1-1-1-11111111111-1-1-1-111-1-111-1-11-1-111111111-1-111-1-1-1-1-1-1
χ81111111111-1-11111111111-1-11-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11-111-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-11-11-11-11-1-111111111-1-1-1-11-1-11
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-111-11-11-11111-1-1-1-11111-1-1-111-1
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11-1-111111-1-111-1-1-1-1-1-111-1-111
χ1311111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-11111111111-1-1-11-1-111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111
χ1411111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-111-1-1-1-11111-1-1-11-1-111-11111-1-111-1-111-1-111-1-1-1-111-1-1
χ1511111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1111-1-1111-1-1-1111111-1-1-1-111-111-1
χ1611111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11-1-111111-1-1-111111-1-1-1-1-1-111111-1-11
χ17222222222222222-1-122-1-1222-122-1-1-122-1-12200000000220000-1-1-1-1-1-1-1-100022020000-1-10000-1-1000-10-1
χ18222222222222222-1-122-1-1222-122-1-1-122-1-12200000000-2-20000-1-1-1-1-1-1-1-1000-2-20-2000011000011000101
χ1922222222222222-122-1-122-122-1-1-1-1-1-1-1-122-1-12222220000-1-1-1-12-1-12-1-1-1-1200000000-1-10000-1-100-1-10000
χ2022222222222222-122-1-122-122-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2000011112-1-12-1-1-1-1-2000000001100001100110000
χ212222222222-2-2222-1-122-1-12-2-2-1-2-2-1-1-1-2-2-1-122000000002200001111-1-111000-220-20000-1-10000-1-1000101
χ222222222222-2-2222-1-122-1-12-2-2-1-2-2-1-1-1-2-2-1-12200000000-2-200001111-1-1110002-202000011000011000-10-1
χ232222222222-2-222-122-1-122-1-2-2-111-1-1-11122-1-12222-2-200001111-211-2-1-111-200000000110000-1-100-1-10000
χ242222222222-2-222-122-1-122-1-2-2-111-1-1-11122-1-1-2-2-2-2220000-1-1-1-1-211-2-1-111200000000-1-100001100110000
χ2522222-2-22222-2-2-22-1-122-1-122-2-122-1-1-1-2-211-2-200000000220000-1-1-1111110002-20-20000110000-1-1000-101
χ2622222-2-22222-2-2-22-1-122-1-122-2-122-1-1-1-2-211-2-200000000-2-20000-1-1-111111000-22020000-1-100001100010-1
χ2722222-2-22222-2-2-2-122-1-122-12-2-1-1-1-1-1-111-2-21122-2-2-2-2000011112-1-1-21111200000000-1-10000-1-100110000
χ2822222-2-22222-2-2-2-122-1-122-12-2-1-1-1-1-1-111-2-211-2-222220000-1-1-1-12-1-1-21111-2000000001100001100-1-10000
χ2922222-2-2222-22-2-22-1-122-1-12-22-1-2-2-1-1-12211-2-200000000220000111-111-1-1000-2-2020000110000-1-100010-1
χ3022222-2-2222-22-2-22-1-122-1-12-22-1-2-2-1-1-12211-2-200000000-2-20000111-111-1-1000220-20000-1-1000011000-101
χ3122222-2-2222-22-2-2-122-1-122-1-22-111-1-1-1-1-1-2-21122-2-2220000-1-1-1-1-211211-1-1-200000000110000-1-100110000
χ3222222-2-2222-22-2-2-122-1-122-1-22-111-1-1-1-1-1-2-211-2-222-2-200001111-211211-1-1200000000-1-100001100-1-10000
χ3322-2-222i−2i2-2-2002i−2i222-22-2-2-2002002-2-2002i−2i2i−2i2-22i−2i000000000000002i−2i000000000000000002-2002i−2i0000
χ3422-2-222i−2i2-2-2002i−2i222-22-2-2-2002002-2-2002i−2i2i−2i-22−2i2i000000000000002i−2i00000000000000000-2200−2i2i0000
χ3522-2-222i−2i2-2-2002i−2i-1221-1-2-2100-1−i3i3-1113−32i−2i−ii2-22i−2i00000033−3−30−i3i30−ii3−3000000000−i3i30000-1100−ii0000
χ3622-2-222i−2i2-2-2002i−2i-1221-1-2-2100-1−i3i3-1113−32i−2i−ii-22−2i2i000000−3−3330−i3i30−ii3−3000000000i3−i300001-100i−i0000
χ3722-2-222i−2i2-2-2002i−2i-1221-1-2-2100-1i3−i3-111−332i−2i−ii2-22i−2i000000−3−3330i3−i30−ii−33000000000i3−i30000-1100−ii0000
χ3822-2-222i−2i2-2-2002i−2i-1221-1-2-2100-1i3−i3-111−332i−2i−ii-22−2i2i00000033−3−30i3−i30−ii−33000000000−i3i300001-100i−i0000
χ3922-2-22−2i2i2-2-200−2i2i222-22-2-2-2002002-2-200−2i2i−2i2i2-2−2i2i00000000000000−2i2i000000000000000002-200−2i2i0000
χ4022-2-22−2i2i2-2-200−2i2i222-22-2-2-2002002-2-200−2i2i−2i2i-222i−2i00000000000000−2i2i00000000000000000-22002i−2i0000
χ4122-2-22−2i2i2-2-200−2i2i-1221-1-2-2100-1−i3i3-111−33−2i2ii−i2-2−2i2i000000−3−3330−i3i30i−i−33000000000−i3i30000-1100i−i0000
χ4222-2-22−2i2i2-2-200−2i2i-1221-1-2-2100-1−i3i3-111−33−2i2ii−i-222i−2i00000033−3−30−i3i30i−i−33000000000i3−i300001-100−ii0000
χ4322-2-22−2i2i2-2-200−2i2i-1221-1-2-2100-1i3−i3-1113−3−2i2ii−i2-2−2i2i00000033−3−30i3−i30i−i3−3000000000i3−i30000-1100i−i0000
χ4422-2-22−2i2i2-2-200−2i2i-1221-1-2-2100-1i3−i3-1113−3−2i2ii−i-222i−2i000000−3−3330i3−i30i−i3−3000000000−i3i300001-100−ii0000
χ452-2-22200-22-2000022-2-2-22-2200200-22-200000000002-22-22-22-22-20000000000000000000002-2002-2000000
χ462-2-22200-22-2000022-2-2-22-2200200-22-200000000002-2-22-222-22-2000000000000000000000-2200-22000000
χ472-2-22200-22-2000022-2-2-22-2200200-22-20000000000-222-2-22-22-220000000000000000000002-200-22000000
χ482-2-22200-22-2000022-2-2-22-2200200-22-20000000000-22-222-2-22-22000000000000000000000-22002-2000000
χ4944444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2-2-2-2-200000000000000-211-211110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-412211122-2-2-2-2000000000000002-1-1211-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-211122222200000000000000-2112-1-1-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-44122111-2-22222000000000000002-1-1-2-1-1110000000000000000000000000
χ5344-4-444i−4i4-4-4004i−4i4-2-2-4422-400-200-22200−2i2i4i−4i000000000000000000−2i2i000000000000000000000000000
χ5444-4-444i−4i4-4-4004i−4i-2-2-22-2222001−2i32i31-1-123−23−2i2i−2i2i000000000000000i3−i30i−i−330000000000000000000000000
χ5544-4-444i−4i4-4-4004i−4i-2-2-22-22220012i3−2i31-1-1−2323−2i2i−2i2i000000000000000−i3i30i−i3−30000000000000000000000000
χ5644-4-44−4i4i4-4-400−4i4i4-2-2-4422-400-200-222002i−2i−4i4i0000000000000000002i−2i000000000000000000000000000
χ5744-4-44−4i4i4-4-400−4i4i-2-2-22-2222001−2i32i31-1-1−23232i−2i2i−2i000000000000000i3−i30−ii3−30000000000000000000000000
χ5844-4-44−4i4i4-4-400−4i4i-2-2-22-22220012i3−2i31-1-123−232i−2i2i−2i000000000000000−i3i30−ii−330000000000000000000000000
χ594-44-4400-4-44000044-44-4-44-400400-4-4400000000000000000000000000000000000000000000000000000
χ604-44-4400-4-4400004-224-42-2-400-20022-2000000000000000000000000000000000000000−2i32i3000000000000
χ614-44-4400-4-4400004-224-42-2-400-20022-20000000000000000000000000000000000000002i3−2i3000000000000
χ624-44-4400-4-440000-24-4-22-44200-20022-2000000000000000023−23−2323000000000000000000000000000000000
χ634-44-4400-4-440000-24-4-22-44200-20022-20000000000000000−232323−23000000000000000000000000000000000
χ644-4-44400-44-400004-22-4-4-22400-2002-22000000000000004-400000000000000000000000000000-22000000
χ654-4-44400-44-400004-22-4-4-22400-2002-2200000000000000-44000000000000000000000000000002-2000000
χ664-4-44400-44-40000-24-4224-4-200-2002-2200000000004-40000-22-22000000000000000000000000000000000
χ674-4-44400-44-40000-24-4224-4-200-2002-220000000000-4400002-22-2000000000000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-300000000000000000022000000000000000220020-1-10000-1-1000000-10-10
χ696666-366-3-3-366-3-300000000-3-3000000000000000000-2-2000000000000000-2-200-20110000110000001010
χ706666-366-3-3-3-6-6-3-30000000033000000000000000000220000000000000002-200-20-1-10000-1-10000001010
χ716666-366-3-3-3-6-6-3-30000000033000000000000000000-2-2000000000000000-22002011000011000000-10-10
χ726666-3-6-6-3-3-36-63300000000-3300000000000000000022000000000000000-2200-20110000-1-1000000-1010
χ736666-3-6-6-3-3-36-63300000000-33000000000000000000-2-20000000000000002-20020-1-100001100000010-10
χ746666-3-6-6-3-3-3-6633000000003-300000000000000000022000000000000000-2-20020110000-1-100000010-10
χ756666-3-6-6-3-3-3-6633000000003-3000000000000000000-2-20000000000000002200-20-1-1000011000000-1010
χ768-88-8800-8-880000-4-44-444-4400200-2-2200000000000000000000000000000000000000000000000000000
χ778-8-88800-88-80000-4-4444-44-400200-22-200000000000000000000000000000000000000000000000000000
χ781212-12-12-612i−12i-66600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ791212-12-12-6−12i12i-666006i−6i000000000000000000000000000000000000000000000000000000000000000000000
χ8012-1212-12-60066-60000000000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ8112-1212-12-60066-600000000000000000000000000000000000000000000000000000002i3−2i30000000000000000
χ8212-12-1212-6006-66000000000000000000000000000000004-4000000000000000000000000000-220000000000
χ8312-12-1212-6006-6600000000000000000000000000000000-440000000000000000000000000002-20000000000

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