Finite Group Databasebeta

← Group #11776295

Character table — Group #11776295

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222444444444444444444444888888888888888888888818181818181824242424242424242424242424242424363636363648484848
order1222334444666666346668888121212121212121212121212121212121212242424242424242424242424242424242244444444888824242424242424244888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111
χ5111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ6111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1
χ8111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11111-1-111
χ9111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-11-11-1i−ii−iii−i−iii−i−i-1ii−i−i1-11-1
χ10111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-11-11−ii−ii−i−iii−i−iii-1ii−i−i-11-11
χ11111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111-1-11i−i−iiii−i−i−i−iii1−i−iii1-1-11
χ12111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111-111-1−iii−i−i−iiiii−i−i1−i−iii-111-1
χ13111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-11-11-1−ii−ii−i−iii−i−iii-1−i−iii1-11-1
χ14111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-11-11i−ii−iii−i−iii−i−i-1−i−iii-11-11
χ15111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111-1-11−iii−i−i−iiiii−i−i1ii−i−i1-1-11
χ16111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111-111-1i−i−iiii−i−i−i−iii1ii−i−i-111-1
χ172222222-22-22222222-22220000-2-222-2-2-2-2-2-222-2-2-2-222000000000000000022-2-2220000000000000000-200000000
χ182222222-22-22222222-22220000-2-222-2-2-2-2-2-222-2-2-2-2220000000000000000-2-222-2-20000000000000000200000000
χ19222222-22-222222222-2222000022-2-2222222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-20000000000000000200000000
χ20222222-22-222222222-2222000022-2-2222222-2-2-2-2-2-2-2-20000000000000000-2-222220000000000000000-200000000
χ2122222-1222222-1-12-1-12-1-1-122222-12-1-1-12-1-1-12-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000002200220000-1-1-1-10000000-1-1
χ2222222-1222222-1-12-1-12-1-1-122222-12-1-1-12-1-1-12-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000-2-200-2-200001111000000011
χ2322222-1222222-1-12-1-12-1-1-1-2-2-2-22-12-1-1-12-1-1-12-12-1-1-1-1-1-2-2111111-2-2111111000000002200-2-2000011110000000-1-1
χ2422222-1222222-1-12-1-12-1-1-1-2-2-2-22-12-1-1-12-1-1-12-12-1-1-1-1-1-2-2111111-2-211111100000000-2-200220000-1-1-1-1000000011
χ2522222-1-2-2-2-222-1-12-1-12-1-1-12i2i−2i−2i-21-2111-2111-212-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii000000002-2002i−2i0000−i−iii0000000-11
χ2622222-1-2-2-2-222-1-12-1-12-1-1-12i2i−2i−2i-21-2111-2111-212-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii00000000-2200−2i2i0000ii−i−i00000001-1
χ2722222-1-2-2-2-222-1-12-1-12-1-1-1−2i−2i2i2i-21-2111-2111-212-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i000000002-200−2i2i0000ii−i−i0000000-11
χ2822222-1-2-2-2-222-1-12-1-12-1-1-1−2i−2i2i2i-21-2111-2111-212-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000-22002i−2i0000−i−iii00000001-1
χ292222-122222-1-122-12-12-1-1-12222-12-12-1-1-12-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000022002200-1-1-1-1000000000-1-100
χ302222-122222-1-122-12-12-1-1-12222-12-12-1-1-12-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000-2-200-2-20011110000000001100
χ312222-122222-1-122-12-12-1-1-1-2-2-2-2-12-12-1-1-12-1-1-12-12-1-1-1-111-2-2111111-2-211110000002200-2-2001111000000000-1-100
χ322222-122222-1-122-12-12-1-1-1-2-2-2-2-12-12-1-1-12-1-1-12-12-1-1-1-111-2-2111111-2-21111000000-2-2002200-1-1-1-10000000001100
χ332222-12-2-2-2-2-1-122-12-12-1-1-12i2i−2i−2i1-21-2111-2111-2-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii0000002-2002i−2i00−i−iii000000000-1100
χ342222-12-2-2-2-2-1-122-12-12-1-1-12i2i−2i−2i1-21-2111-2111-2-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii000000-2200−2i2i00ii−i−i0000000001-100
χ352222-12-2-2-2-2-1-122-12-12-1-1-1−2i−2i2i2i1-21-2111-2111-2-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i0000002-200−2i2i00ii−i−i000000000-1100
χ362222-12-2-2-2-2-1-122-12-12-1-1-1−2i−2i2i2i1-21-2111-2111-2-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i000000-22002i−2i00−i−iii0000000001-100
χ372-2-222220-20-2-2-2-222202-2-2−i2i2−i2i20022000000-2-200002-2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2i22-2002-200000000000000000−i2i2−i2i20000
χ382-2-222220-20-2-2-2-222202-2-2−i2i2−i2i20022000000-2-200002-2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2-2200-2200000000000000000i2−i2i2−i20000
χ392-2-222220-20-2-2-2-222202-2-2i2−i2i2−i20022000000-2-200002-2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i22-2002-200000000000000000i2−i2i2−i20000
χ402-2-222220-20-2-2-2-222202-2-2i2−i2i2−i20022000000-2-200002-2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2-2200-2200000000000000000−i2i2−i2i20000
χ412-2-2222-2020-2-2-2-222202-2-22−2−2200-2-2000000220000-222−22−222−2−2−22−22−2−2222-200-22000000000000000002−2−220000
χ422-2-2222-2020-2-2-2-222202-2-22−2−2200-2-2000000220000-222−22−222−2−2−22−22−2−222-22002-200000000000000000−222−20000
χ432-2-2222-2020-2-2-2-222202-2-2−222−200-2-2000000220000-22−22−22−2−2222−22−222−2−22-200-2200000000000000000−222−20000
χ442-2-2222-2020-2-2-2-222202-2-2−222−200-2-2000000220000-22−22−22−2−2222−22−222−2−2-22002-2000000000000000002−2−220000
χ4544444-24-44-444-2-24-2-2-4-2-2-20000-424-222-42224-2-4222-2-200000000000000000000000000000000000000000000000
χ4644444-2-44-4444-2-24-2-2-4-2-2-200004-2-42-2-24-2-2-2-42-42222200000000000000000000000000000000000000000000000
χ474444-244-44-4-2-244-24-2-4-2-2-200002-4-24222-422-242-422-2-200000000000000000000000000000000000000000000000
χ484444-24-44-44-2-244-24-2-4-2-2-20000-242-4-2-2-24-2-22-42-4222200000000000000000000000000000000000000000000000
χ494444-2-24444-2-2-2-2-2-2141114444-2-2-2-211-2-211-2-2-2-21111-2-2-2-21111-2-2-2-211110000000000000000000000000000000
χ504444-2-24444-2-2-2-2-2-214111-4-4-4-4-2-2-2-211-2-211-2-2-2-211112222-1-1-1-12222-1-1-1-10000000000000000000000000000000
χ514444-2-24-44-4-2-2-2-2-2-21-4111000022-2-2-1-122-1-1-2-222-1-11100003i−3i3i−3i00003i−3i3i−3i0000000000000000000000000000000
χ524444-2-24-44-4-2-2-2-2-2-21-4111000022-2-2-1-122-1-1-2-222-1-1110000−3i3i−3i3i0000−3i3i−3i3i0000000000000000000000000000000
χ534444-2-2-44-44-2-2-2-2-2-21-41110000-2-22211-2-2112222-1-1-1-100003-33-30000-33-330000000000000000000000000000000
χ544444-2-2-44-44-2-2-2-2-2-21-41110000-2-22211-2-2112222-1-1-1-10000-33-3300003-33-30000000000000000000000000000000
χ554444-2-2-4-4-4-4-2-2-2-2-2-2141114i4i−4i−4i2222-1-122-1-122-2-211-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000000
χ564444-2-2-4-4-4-4-2-2-2-2-2-214111−4i−4i4i4i2222-1-122-1-122-2-211-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000000
χ5744-4-44400004-44-4-4-440-44-400000000000000000000000000000000000000004-4000000000000000000000000000
χ5844-4-44400004-44-4-4-440-44-40000000000000000000000000000000000000000-44000000000000000000000000000
χ594-44-444040-4-44-44-4-440-4-440000-4-400-4-444440000000000000000000000000000000000000000000000000000000
χ604-44-4440-404-44-44-4-440-4-440000440044-4-4-4-40000000000000000000000000000000000000000000000000000000
χ614-44-44-2040-4-442-2-42-2022-20000-4200224-2-2-20000000000000000000000000000000000000000006−66−6000000000
χ624-44-44-2040-4-442-2-42-2022-20000-4200224-2-2-2000000000000000000000000000000000000000000−66−66000000000
χ634-44-44-20-404-442-2-42-2022-200004-200-2-2-4222000000000000000000000000000000000000000000i6−i6−i6i6000000000
χ644-44-44-20-404-442-2-42-2022-200004-200-2-2-4222000000000000000000000000000000000000000000−i6i6i6−i6000000000
χ654-44-4-24040-42-2-442-4-2022-200002-40022-24-2-2000000000000000000000000000000000000006−66−60000000000000
χ664-44-4-24040-42-2-442-4-2022-200002-40022-24-2-200000000000000000000000000000000000000−66−660000000000000
χ674-44-4-240-4042-2-442-4-2022-20000-2400-2-22-42200000000000000000000000000000000000000i6−i6−i6i60000000000000
χ684-44-4-240-4042-2-442-4-2022-20000-2400-2-22-42200000000000000000000000000000000000000−i6i6i6−i60000000000000
χ694-4-444-240-40-4-4224-2-20-222−2i22i2−2i22i2004-2000000-420000-22−2i22i2i2−i2i2i2−i2−i2−2i22i2i2−i2i2i2−i2−i20000000000000000000000000000000
χ704-4-444-240-40-4-4224-2-20-2222i2−2i22i2−2i2004-2000000-420000-222i2−2i2−i2i2−i2−i2i2i22i2−2i2−i2i2−i2−i2i2i20000000000000000000000000000000
χ714-4-444-2-4040-4-4224-2-20-22222−22−222200-420000004-200002-222−22−22−2−222−22222−222−2−20000000000000000000000000000000
χ724-4-444-2-4040-4-4224-2-20-222−222222−2200-420000004-200002-2−22222−222−2−222−22−22−2−2220000000000000000000000000000000
χ734-4-44-2440-4022-4-4-24-20-222−2i22i2−2i22i200-240000002-40000-22i2−i2−2i22i2i2i2−i2−i2i2−i2−2i22i2i2i2−i2−i20000000000000000000000000000000
χ744-4-44-2440-4022-4-4-24-20-2222i2−2i22i2−2i200-240000002-40000-22−i2i22i2−2i2−i2−i2i2i2−i2i22i2−2i2−i2−i2i2i20000000000000000000000000000000
χ754-4-44-24-404022-4-4-24-20-22222−22−2222002-4000000-2400002-2−2222−22−2−2222−2−222222−2−20000000000000000000000000000000
χ764-4-44-24-404022-4-4-24-20-222−222222−22002-4000000-2400002-22−2−222222−2−2−2222−22−2−2220000000000000000000000000000000
χ774-4-44-2-240-402222-2-2101-1-1−2i22i2−2i22i200-2-23i−3i003i−3i22003i−3i1-1i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ230000000000000000000000000000000
χ784-4-44-2-240-402222-2-2101-1-1−2i22i2−2i22i200-2-2−3i3i00−3i3i2200−3i3i1-1i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ230000000000000000000000000000000
χ794-4-44-2-240-402222-2-2101-1-12i2−2i22i2−2i200-2-23i−3i003i−3i22003i−3i1-1−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ230000000000000000000000000000000
χ804-4-44-2-240-402222-2-2101-1-12i2−2i22i2−2i200-2-2−3i3i00−3i3i2200−3i3i1-1−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ230000000000000000000000000000000
χ814-4-44-2-2-40402222-2-2101-1-122−22−222200223i−3i003i−3i-2-200−3i3i-11−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ232−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ230000000000000000000000000000000
χ824-4-44-2-2-40402222-2-2101-1-122−22−22220022−3i3i00−3i3i-2-2003i−3i-11−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ230000000000000000000000000000000
χ834-4-44-2-2-40402222-2-2101-1-1−222222−2200223i−3i003i−3i-2-200−3i3i-112−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ230000000000000000000000000000000
χ844-4-44-2-2-40402222-2-2101-1-1−222222−220022−3i3i00−3i3i-2-2003i−3i-112−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ230000000000000000000000000000000
χ8588-8-88-400008-8-44-84-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-480000-448-84-8-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-40000-44-444420-22-2000000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-40000-44-444420-22-200000000−6i6i006i−6i0000000000000000000000000000000000000000000000000000000
χ898-88-8-4-4080-84-44-44420-2-2200004400-2-2-4-4220000000000000000000000000000000000000000000000000000000
χ908-88-8-4-40-8084-44-44420-2-220000-4-4002244-2-20000000000000000000000000000000000000000000000000000000

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