Finite Group Databasebeta

← Group #11780256

Character table — Group #11780256

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444444444888888888888888888888888121224242424242424242424242424363636363636484848484872
order12223344446666663466612121212121212121212121288121212121212242424242424242424242424242424244424466881212242424244488884121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-1-1-1111
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111111-1-11111-1-1-1-1-1-1
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111-1-11
χ92222222-22-22222222-2222-2-2-222222222-200-2-2-2-2-2-2000000000000000022-200-2-200220000000000000000
χ102222222-22-22222222-2222-2-2-222222222-200-2-2-2-2-2-20000000000000000-2-22002200-2-20000000000000000
χ11222222-22-222222222-2222222-2-2-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000000022000000000-2
χ12222222-22-222222222-2222222-2-2-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000000-2-20000000002
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-22200000000000000000002-200000000000000000002-20
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-2220000000000000000000-220000000000000000000-220
χ1522222-1222222-1-12-1-12-1-1-12-1-12-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122200-1-100-1-100000000002-1-1000
χ1622222-1222222-1-12-1-12-1-1-12-1-12-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2001100110000000000-211000
χ1722222-1222222-1-12-1-12-1-1-12-1-12-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-211111111111122200-1-100-1-10000000000-211000
χ1822222-1222222-1-12-1-12-1-1-12-1-12-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-2111111111111-2-2-20011001100000000002-1-1000
χ1922222-12-22-222-1-12-1-1-2-1-1-1-2112-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i322-2001100-1-100000000000−i3i3000
χ2022222-12-22-222-1-12-1-1-2-1-1-1-2112-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-2200-1-1001100000000000i3−i3000
χ2122222-12-22-222-1-12-1-1-2-1-1-1-2112-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i322-2001100-1-100000000000i3−i3000
χ2222222-12-22-222-1-12-1-1-2-1-1-1-2112-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-2200-1-1001100000000000−i3i3000
χ232222-122222-1-122-12-12-1-1-1-122-12-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100022002200-1-1-1-1000000000-1-10
χ242222-122222-1-122-12-12-1-1-1-122-12-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1000-2-200-2-2001111000000000110
χ252222-122222-1-122-12-12-1-1-1-122-12-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-211110002200-2-2001111000000000-1-10
χ262222-122222-1-122-12-12-1-1-1-122-12-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-21111000-2-2002200-1-1-1-1000000000110
χ272222-12-2-2-2-2-1-122-12-12-1-1-11-2-21-2111-211100-1211-1-133−3−30033−3−30033−3−30002-200000033−3−3000000000-110
χ282222-12-2-2-2-2-1-122-12-12-1-1-11-2-21-2111-211100-1211-1-133−3−30033−3−30033−3−3000-22000000−3−3330000000001-10
χ292222-12-2-2-2-2-1-122-12-12-1-1-11-2-21-2111-211100-1211-1-1−3−33300−3−33300−3−3330002-2000000−3−333000000000-110
χ302222-12-2-2-2-2-1-122-12-12-1-1-11-2-21-2111-211100-1211-1-1−3−33300−3−33300−3−333000-2200000033−3−30000000001-10
χ312-22-2220-2022-2-22-2-2202-2-2-22-2000000002−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000002i−2i22−2−2000000
χ322-22-2220-2022-2-22-2-2202-2-2-22-2000000002−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000−2i2i−2−222000000
χ332-22-2220-2022-2-22-2-2202-2-2-22-2000000002i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000002i−2i−2−222000000
χ342-22-2220-2022-2-22-2-2202-2-2-22-2000000002i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000−2i2i22−2−2000000
χ352-2-222220-20-2-2-2-22220-22-20002222-2-2-2-200000000000000000000000002i−2i00000−i2i22i−2i−i2i2−i2i2002−22−2000000
χ362-2-222220-20-2-2-2-22220-22-20002222-2-2-2-200000000000000000000000002i−2i00000i2−i22i−2ii2−i2i2−i200−22−22000000
χ372-2-222220-20-2-2-2-22220-22-20002222-2-2-2-20000000000000000000000000−2i2i00000−i2i2−2i2i−i2i2−i2i200−22−22000000
χ382-2-222220-20-2-2-2-22220-22-20002222-2-2-2-20000000000000000000000000−2i2i00000i2−i2−2i2ii2−i2i2−i2002−22−2000000
χ3944444-2-44-4444-2-24-2-2-4-2-2-24-2-2-4222-4222400-42-2-2220000000000000000000000000000000000000000000
χ4044444-2-4-4-4-444-2-24-2-24-2-2-2-422-4222-4222-4004-222-2-20000000000000000000000000000000000000000000
χ414444-244-44-4-2-244-24-2-4-2-2-22-4-4-24-2-2-24-2-22002-422220000000000000000000000000000000000000000000
χ424444-24-44-44-2-244-24-2-4-2-2-2-2442-4222-422-2002-4-2-2220000000000000000000000000000000000000000000
χ434444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-244-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000
χ444444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-2-4-4-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000
χ454444-2-24-44-4-2-2-2-2-2-21-4111222-2-211-2-21120022-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000000
χ464444-2-24-44-4-2-2-2-2-2-21-4111222-2-211-2-21120022-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000000
χ474444-2-2-44-44-2-2-2-2-2-21-4111-2-2-222-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000
χ484444-2-2-44-44-2-2-2-2-2-21-4111-2-2-222-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000
χ494444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1112323−23−2300−3−33300−3−333000000000000000000000000000
χ504444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-111−23−2323230033−3−30033−3−3000000000000000000000000000
χ5144-4-4440000-444-4-4-440-4-44000000000000000000000000000000000000000000000000000002-2-22000000
χ5244-4-4440000-444-4-4-440-4-4400000000000000000000000000000000000000000000000000000-222-2000000
χ534-44-444040-44-4-44-4-4404-4-44-4400000000-40000-44000000000000000000000000000000000000000000000
χ544-44-44-2040-44-42-2-42-20-22242-200000000-400002-20000006−66−66−6−66−66−66000000000000000000000000000
χ554-44-44-2040-44-42-2-42-20-22242-200000000-400002-2000000−66−66−666−66−66−6000000000000000000000000000
χ564-44-44-20-4044-42-2-42-20-222-4-22000000004−2i22i200-2200−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000000
χ574-44-44-20-4044-42-2-42-20-222-4-220000000042i2−2i200-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000000
χ584-44-4-24040-4-22-442-4-20-222-2-4400000000200002-200i6−i6−i6i600i6−i6−i6i600i6−i6−i6i6000000000000000000000000000
χ594-44-4-24040-4-22-442-4-20-222-2-4400000000200002-200−i6i6i6−i600−i6i6i6−i600−i6i6i6−i6000000000000000000000000000
χ604-44-4-240-404-22-442-4-20-22224-400000000-2−2i22i200-2200i2−i2i2−i2−2i22i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000000
χ614-44-4-240-404-22-442-4-20-22224-400000000-22i2−2i200-2200−i2i2−i2i22i2−2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000000
χ624-44-4-2-2040-4-222-222101-1-1-22-2003i−3i003i−3i20000-113i−3ii6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ634-44-4-2-2040-4-222-222101-1-1-22-2003i−3i003i−3i20000-113i−3i−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ644-44-4-2-2040-4-222-222101-1-1-22-200−3i3i00−3i3i20000-11−3i3ii6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ654-44-4-2-2040-4-222-222101-1-1-22-200−3i3i00−3i3i20000-11−3i3i−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ664-44-4-2-20-404-222-222101-1-12-22003i−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+2ζ23000000000000000000000000000
χ674-44-4-2-20-404-222-222101-1-12-22003i−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+ζ13−2ζ23000000000000000000000000000
χ684-44-4-2-20-404-222-222101-1-12-2200−3i3i00−3i3i-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−ζ23000000000000000000000000000
χ694-44-4-2-20-404-222-222101-1-12-2200−3i3i00−3i3i-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+ζ23000000000000000000000000000
χ704-4-4444-4040-4-4-4-44440-44-4000-4-4-4-444440000000000000000000000000000000000000000000000000000
χ714-4-444-240-40-4-4224-2-202-220004-2-2-2-422200000000000000000000000004i−4i0000000−2i2i0000000000000000
χ724-4-444-240-40-4-4224-2-202-220004-2-2-2-42220000000000000000000000000−4i4i00000002i−2i0000000000000000
χ734-4-444-2-4040-4-4224-2-202-22000-42224-2-2-2000000000000000000000000000000−2i32i300000000000000000000
χ744-4-444-2-4040-4-4224-2-202-22000-42224-2-2-20000000000000000000000000000002i3−2i300000000000000000000
χ754-4-44-2440-4022-4-4-24-202-22000-24-2-22-42200000000000000000000000000000000−2i22i200i2−i2i2−i2000000000000
χ764-4-44-2440-4022-4-4-24-202-22000-24-2-22-422000000000000000000000000000000002i2−2i200−i2i2−i2i2000000000000
χ774-4-44-24-404022-4-4-24-202-220002-422-24-2-2000000000000000000000000000000000000i6−i6−i6i6000000000000
χ784-4-44-24-404022-4-4-24-202-220002-422-24-2-2000000000000000000000000000000000000−i6i6i6−i6000000000000
χ7988-8-88-40000-88-44-84-4044-4000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8-4800004-48-84-8-4044-4000000000000000000000000000000000000000000000000000000000000000
χ8188-8-8-4-400004-4-444420-2-22000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000
χ8288-8-8-4-400004-4-444420-2-2200000−6i6i006i−6i0000000000000000000000000000000000000000000000000000
χ838-8-88-4-480-804444-4-420-22-2000-4-42244-2-20000000000000000000000000000000000000000000000000000
χ848-8-88-4-4-80804444-4-420-22-200044-2-2-4-4220000000000000000000000000000000000000000000000000000

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