Finite Group Databasebeta

← Group #11781856

Character table — Group #11781856

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222244444444444444444888888888888888888888888242424242424242424242424363636364848484848487272
order12223344446666663466612121212121212121212121288121212121212242424242424242424242424242424242466881212242424248888441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-11-1-11111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ92222222-2-222222222-22222-2-2-22222222-200-2-2-2-2-2-200000000000000002-22200-2-20000000000000000
χ102222222-2-222222222-22222-2-2-22222222-200-2-2-2-2-2-20000000000000000-22-2-200220000000000000000
χ11222222-222-22222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000022-2-200000000
χ12222222-222-22222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000-2-22200000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000002i−2i002i2i−2i−2i000000000000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-22200000000000000000000−2i2i00−2i−2i2i2i000000000000
χ1522222-1222222-1-12-1-12-1-1-122-1-1-1-1-12-1-1-1222-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-100-1-10000000020-1-10000
χ1622222-1222222-1-12-1-12-1-1-122-1-1-1-1-12-1-1-1222-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211001100000000-20110000
χ1722222-1222222-1-12-1-12-1-1-122-1-1-1-1-12-1-1-12-2-2-12-1-1-1-1-2-2-2-211111111111122-1-100-1-100000000-20110000
χ1822222-1222222-1-12-1-12-1-1-122-1-1-1-1-12-1-1-12-2-2-12-1-1-1-1-2-2-2-2111111111111-2-21100110000000020-1-10000
χ1922222-12-2-2222-1-12-1-1-2-1-1-12-211-1-1-12-1-1-1-2001-211110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i32-2-1-100110000000000−i3i30000
χ2022222-12-2-2222-1-12-1-1-2-1-1-12-211-1-1-12-1-1-1-2001-211110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-221100-1-10000000000i3−i30000
χ2122222-12-2-2222-1-12-1-1-2-1-1-12-211-1-1-12-1-1-1-2001-211110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i32-2-1-100110000000000i3−i30000
χ2222222-12-2-2222-1-12-1-1-2-1-1-12-211-1-1-12-1-1-1-2001-211110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-221100-1-10000000000−i3i30000
χ232222-122222-1-122-12-12-1-1-1-1-1222-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100002200-1-1-1-100000200-1-100
χ242222-122222-1-122-12-12-1-1-1-1-1222-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-200111100000-2001100
χ252222-122222-1-122-12-12-1-1-1-1-1222-1-1-12-1-1-1-2-22-1-1-1-1-11111-2-21111-2-2111100002200-1-1-1-100000-2001100
χ262222-122222-1-122-12-12-1-1-1-1-1222-1-1-12-1-1-1-2-22-1-1-1-1-11111-2-21111-2-211110000-2-200111100000200-1-100
χ272222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2111-2111002-111-1-133−3−30033−3−30033−3−300002i−2i00−i−iii00000000−i3i300
χ282222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2111-2111002-111-1-133−3−30033−3−30033−3−30000−2i2i00ii−i−i00000000i3−i300
χ292222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2111-2111002-111-1-1−3−33300−3−33300−3−33300002i−2i00−i−iii00000000i3−i300
χ302222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2111-2111002-111-1-1−3−33300−3−33300−3−3330000−2i2i00ii−i−i00000000−i3i300
χ3122-2-2220-2202-2-22-2-2202-2-20-22-200000002−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000002-2000000−i2i2
χ3222-2-2220-2202-2-22-2-2202-2-20-22-200000002−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000-22000000i2−i2
χ3322-2-2220-2202-2-22-2-2202-2-20-22-200000002i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000002-2000000i2−i2
χ3422-2-2220-2202-2-22-2-2202-2-20-22-200000002i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000-22000000−i2i2
χ3544444-2-444-444-2-24-2-2-4-2-2-2-44-2-2222-42224002-4-2-2220000000000000000000000000000000000000000
χ3644444-2-4-4-4-444-2-24-2-24-2-2-2-4-422222-4222-400-2422-2-20000000000000000000000000000000000000000
χ374444-244-4-44-2-244-24-2-4-2-2-2-22-4-44-2-2-24-2-2200-4222220000000000000000000000000000000000000000
χ384444-24-444-4-2-244-24-2-4-2-2-22-244-4222-422-200-42-2-2220000000000000000000000000000000000000000
χ394444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-244-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000000
χ404444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-2-4-4-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000000
χ414444-2-24-4-44-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000
χ424444-2-24-4-44-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000
χ434444-2-2-444-4-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000
χ444444-2-2-444-4-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000
χ454444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1112323−23−2300−3−33300−3−333000000000000000000000000
χ464444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-111−23−2323230033−3−30033−3−3000000000000000000000000
χ4744-4-44404-404-4-44-4-4404-4-404-440000000-40000-44000000000000000000000000000000000000000000
χ4844-4-44-204-404-42-2-42-20-222042-20000000-400002-20000006−66−66−6−66−66−66000000000000000000000000
χ4944-4-44-204-404-42-2-42-20-222042-20000000-400002-2000000−66−66−666−66−66−6000000000000000000000000
χ5044-4-44-20-4404-42-2-42-20-2220-4-2200000004−2i22i200-2200−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ5144-4-44-20-4404-42-2-42-20-2220-4-22000000042i2−2i200-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ5244-4-4-2404-40-22-442-4-20-2220-2-440000000200002-200i6−i6−i6i600i6−i6−i6i600i6−i6−i6i6000000000000000000000000
χ5344-4-4-2404-40-22-442-4-20-2220-2-440000000200002-200−i6i6i6−i600−i6i6i6−i600−i6i6i6−i6000000000000000000000000
χ5444-4-4-240-440-22-442-4-20-222024-40000000-2−2i22i200-2200i2−i2i2−i2−2i22i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000
χ5544-4-4-240-440-22-442-4-20-222024-40000000-22i2−2i200-2200−i2i2−i2i22i2−2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000
χ5644-4-4-2-204-40-222-222101-1-10-22-203i−3i003i−3i20000-113i−3ii6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ5744-4-4-2-204-40-222-222101-1-10-22-203i−3i003i−3i20000-113i−3i−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ5844-4-4-2-204-40-222-222101-1-10-22-20−3i3i00−3i3i20000-11−3i3ii6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ5944-4-4-2-204-40-222-222101-1-10-22-20−3i3i00−3i3i20000-11−3i3i−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ6044-4-4-2-20-440-222-222101-1-102-2203i−3i003i−3i-2−2i22i2001-1−3i3ii2−i2i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23000000000000000000000000
χ6144-4-4-2-20-440-222-222101-1-102-2203i−3i003i−3i-22i2−2i2001-1−3i3i−i2i2−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23000000000000000000000000
χ6244-4-4-2-20-440-222-222101-1-102-220−3i3i00−3i3i-2−2i22i2001-13i−3ii2−i2i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23000000000000000000000000
χ6344-4-4-2-20-440-222-222101-1-102-220−3i3i00−3i3i-22i2−2i2001-13i−3i−i2i2−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000000
χ644-44-4440000-4-44-44-440-44-4000000000000000000000000000000000000000000000000−2i22i20000000000
χ654-44-4440000-4-44-44-440-44-40000000000000000000000000000000000000000000000002i2−2i20000000000
χ664-4-4444400-4-44-4-4-4440-4-444000444-4-4-4-40000000000000000000000000000000000000000000000000
χ674-4-4444-4004-44-4-4-4440-4-44-4000-4-4-444440000000000000000000000000000000000000000000000000
χ684-4-444-2400-4-4422-4-2-2022-24000-2-2-2-4222000000000000000000000000000000023−230000000000000000
χ694-4-444-2400-4-4422-4-2-2022-24000-2-2-2-42220000000000000000000000000000000−23230000000000000000
χ704-4-444-2-4004-4422-4-2-2022-2-40002224-2-2-2000000000000000000000000000−2i32i300000000000000000000
χ714-4-444-2-4004-4422-4-2-2022-2-40002224-2-2-20000000000000000000000000002i3−2i300000000000000000000
χ724-4-44-24400-42-2-4-424-2022-2-20004-2-22-422000000000000000000000000000000000i6−i6i6−i6000000000000
χ734-4-44-24400-42-2-4-424-2022-2-20004-2-22-422000000000000000000000000000000000−i6i6−i6i6000000000000
χ744-4-44-24-40042-2-4-424-2022-22000-422-24-2-20000000000000000000000000000000006−6−66000000000000
χ754-4-44-24-40042-2-4-424-2022-22000-422-24-2-2000000000000000000000000000000000−666−6000000000000
χ768-88-88-40000-8-8-4484-404-44000000000000000000000000000000000000000000000000000000000000
χ778-88-8-480000448-8-4-8-404-44000000000000000000000000000000000000000000000000000000000000
χ788-88-8-4-4000044-44-4420-22-2000006i−6i00−6i6i0000000000000000000000000000000000000000000000000
χ798-88-8-4-4000044-44-4420-22-200000−6i6i006i−6i0000000000000000000000000000000000000000000000000
χ808-8-88-4-4800-84-4444-420-2-22-4000-42244-2-20000000000000000000000000000000000000000000000000
χ818-8-88-4-4-80084-4444-420-2-2240004-2-2-4-4220000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.