Finite Group Databasebeta

← Group #11781685

Character table — Group #11781685

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222244444444444444444888888888888888888888888242424242424242424242424363636364848484848487272
order12223344446666663466612121212121212121212121288121212121212242424242424242424242424242424244488121212122424242488882466121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11-111-1-1-1-1
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
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111-1-111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-11111
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
χ92222222-2-222222222-22222-22-2-2222222-200-2-2-2-2-2-200000000000000002-20022-2-20000000000000000
χ102222222-2-222222222-22222-22-2-2222222-200-2-2-2-2-2-20000000000000000-2200-2-2220000000000000000
χ11222222-222-22222222-2222-22-222-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000022-2-200000000
χ12222222-222-22222222-2222-22-222-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000-2-22200000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-2220000000000000000002i−2i00002i2i−2i−2i000000000000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000−2i2i0000−2i−2i2i2i000000000000
χ1522222-12222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-122-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220000-1-1-1-1000020-1-10000
χ1622222-12222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-122-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2000011110000-20110000
χ1722222-12222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-1-2-2-12-1-1-1-1-2-2-2-211111111111100220000-1-1-1-10000-20110000
χ1822222-12222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-1-2-2-12-1-1-1-1-2-2-2-211111111111100-2-200001111000020-1-10000
χ1922222-1-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-10000333333−3−3−3−3−3−3002i−2i0000−i−iii000000−i3i30000
χ2022222-1-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-10000333333−3−3−3−3−3−300−2i2i0000ii−i−i000000i3−i30000
χ2122222-1-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-10000−3−3−3−3−3−3333333002i−2i0000−i−iii000000i3−i30000
χ2222222-1-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-10000−3−3−3−3−3−333333300−2i2i0000ii−i−i000000−i3i30000
χ232222-122222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12200-1-1-1-1000000000200-1-100
χ242222-122222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2001111000000000-2001100
χ252222-122222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12-2-22-1-1-1-1-11111-2-21111-2-211112200-1-1-1-1000000000-2001100
χ262222-122222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12-2-22-1-1-1-1-11111-2-21111-2-21111-2-2001111000000000200-1-100
χ272222-122-2-22222-1-1-1-1-2-1-1-12-2-111-1-12-1-1-1-200-211111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i32-200-1-111000000000000−i3i300
χ282222-122-2-22222-1-1-1-1-2-1-1-12-2-111-1-12-1-1-1-200-211111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-220011-1-1000000000000i3−i300
χ292222-122-2-22222-1-1-1-1-2-1-1-12-2-111-1-12-1-1-1-200-211111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i32-200-1-111000000000000i3−i300
χ302222-122-2-22222-1-1-1-1-2-1-1-12-2-111-1-12-1-1-1-200-211111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-220011-1-1000000000000−i3i300
χ312-2-222202-202-2-2-2-22202-2-20202-2000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000002-200000000−i2i2
χ322-2-222202-202-2-2-2-22202-2-20202-2000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000-2200000000i2−i2
χ332-2-222202-202-2-2-2-22202-2-20202-2000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000002-200000000i2−i2
χ342-2-222202-202-2-2-2-22202-2-20202-2000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000-2200000000−i2i2
χ3544444-24-4-44-2-2-2444-2-4-2-2-2-224-4-4-2-2-24-2-22002-422220000000000000000000000000000000000000000
χ3644444-2-444-4-2-2-2444-2-4-2-2-22-2-444222-422-2002-4-2-2220000000000000000000000000000000000000000
χ374444-24-444-4444-2-2-2-2-4-2-2-2-442-2-222-4222400-42-2-2220000000000000000000000000000000000000000
χ384444-24-4-4-4-4444-2-2-2-24-2-2-2-4-422222-4222-4004-222-2-20000000000000000000000000000000000000000
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
χ414444-2-24-4-44-2-2-2-2-2-21-4111-22-22211-2-21120022-1-1-1-1−2i3−2i32i32i300i3i3−i3−i300i3i3−i3−i3000000000000000000000000
χ424444-2-24-4-44-2-2-2-2-2-21-4111-22-22211-2-21120022-1-1-1-12i32i3−2i3−2i300−i3−i3i3i300−i3−i3i3i3000000000000000000000000
χ434444-2-2-444-4-2-2-2-2-2-21-41112-22-2-2-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000
χ444444-2-2-444-4-2-2-2-2-2-21-41112-22-2-2-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000
χ454444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-11100002323−3−3−3−3−23−233333000000000000000000000000
χ464444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1110000−23−2333332323−3−3−3−3000000000000000000000000
χ4744-4-4440000-44-44-4-440-44-400000000000000000000000000000000000000000000000000−2i22i200000000
χ4844-4-4440000-44-44-4-440-44-4000000000000000000000000000000000000000000000000002i2−2i200000000
χ494-44-444400-4-4-44-44-440-4-444040044-4-4-4-40000000000000000000000000000000000000000000000000
χ504-44-444-4004-4-44-44-440-4-44-40-400-4-444440000000000000000000000000000000000000000000000000
χ514-44-44-2400-422-2-44-4-2022-2-20400-2-22-4220000000000000000000000000000000006−66−6000000000000
χ524-44-44-2400-422-2-44-4-2022-2-20400-2-22-422000000000000000000000000000000000−66−66000000000000
χ534-44-44-2-400422-2-44-4-2022-220-40022-24-2-2000000000000000000000000000000000i6−i6−i6i6000000000000
χ544-44-44-2-400422-2-44-4-2022-220-40022-24-2-2000000000000000000000000000000000−i6i6i6−i6000000000000
χ554-44-4-24400-4-4-442-22-2022-240-200-2-2-42220000000000000000000000000000000−2i32i30000000000000000
χ564-44-4-24400-4-4-442-22-2022-240-200-2-2-422200000000000000000000000000000002i3−2i30000000000000000
χ574-44-4-24-4004-4-442-22-2022-2-40200224-2-2-20000000000000000000000000000023−23000000000000000000
χ584-44-4-24-4004-4-442-22-2022-2-40200224-2-2-200000000000000000000000000000−2323000000000000000000
χ594-4-44440-4404-4-4-4-44404-4-40-40-4400000040000-44000000000000000000000000000000000000000000
χ604-4-444-204-40-222-4-44-20-2220-204-40000002−2i22i200-2200−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ614-4-444-204-40-222-4-44-20-2220-204-400000022i2−2i200-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ624-4-444-20-440-222-4-44-20-222020-44000000-200002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000
χ634-4-444-20-440-222-4-44-20-222020-44000000-200002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000
χ644-4-44-2404-404-4-422-2-20-222040-22000000-4−2i22i200-2200i2−i2i2−i2−2i22i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000
χ654-4-44-2404-404-4-422-2-20-222040-22000000-42i2−2i200-2200−i2i2−i2i22i2−2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000
χ664-4-44-240-4404-4-422-2-20-2220-402-2000000400002-2006−6−66006−6−66006−6−66000000000000000000000000
χ674-4-44-240-4404-4-422-2-20-2220-402-2000000400002-200−666−600−666−600−666−6000000000000000000000000
χ684-4-44-2-204-40-22222-2101-1-10-20-223i−3i003i−3i2−2i22i2001-13i−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
χ694-4-44-2-204-40-22222-2101-1-10-20-223i−3i003i−3i22i2−2i2001-13i−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
χ704-4-44-2-204-40-22222-2101-1-10-20-22−3i3i00−3i3i2−2i22i2001-1−3i3ii2−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
χ714-4-44-2-204-40-22222-2101-1-10-20-22−3i3i00−3i3i22i2−2i2001-1−3i3i−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
χ724-4-44-2-20-440-22222-2101-1-10202-23i−3i003i−3i-20000-11−3i3i6−6−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ734-4-44-2-20-440-22222-2101-1-10202-23i−3i003i−3i-20000-11−3i3i−666−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ744-4-44-2-20-440-22222-2101-1-10202-2−3i3i00−3i3i-20000-113i−3i6−6−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ754-4-44-2-20-440-22222-2101-1-10202-2−3i3i00−3i3i-20000-113i−3i−666−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ7688-8-88-400004-448-8-8-404-44000000000000000000000000000000000000000000000000000000000000
χ7788-8-8-480000-88-8-444-404-44000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-4-400004-44-44420-22-2000006i−6i00−6i6i0000000000000000000000000000000000000000000000000
χ7988-8-8-4-400004-44-44420-22-200000−6i6i006i−6i0000000000000000000000000000000000000000000000000
χ808-88-8-4-4800-844-44-4420-2-22-40-4002244-2-20000000000000000000000000000000000000000000000000
χ818-88-8-4-4-800844-44-4420-2-2240400-2-2-4-4220000000000000000000000000000000000000000000000000

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