Finite Group Databasebeta

← Group #11779545

Character table — Group #11779545

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444444444888888888888888888888888121224242424242424242424242424363636363636484848484872
order12223344446666663466612121212121212121212121288121212121212242424242424242424242424242424242244466881212242424244488884121212122
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
χ92222222-2-222222222-22222-222-2-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000000022000000000-2
χ102222222-2-222222222-22222-222-2-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000000-2-20000000002
χ11222222-222-22222222-2222-22-2-22222222-200-2-2-2-2-2-2000000000000000022-2002200-2-20000000000000000
χ12222222-222-22222222-2222-22-2-22222222-200-2-2-2-2-2-20000000000000000-2-2200-2-200220000000000000000
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
χ1522222-1222222-1-12-1-12-1-1-12-1-1-12-1-1-12-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122200-1-100-1-100000000002-1-1000
χ1622222-1222222-1-12-1-12-1-1-12-1-1-12-1-1-12-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2001100110000000000-211000
χ1722222-1222222-1-12-1-12-1-1-12-1-1-12-1-1-12-1-12-2-22-1-1-1-1-1-2-2-2-211111111111122200-1-100-1-10000000000-211000
χ1822222-1222222-1-12-1-12-1-1-12-1-1-12-1-1-12-1-12-2-22-1-1-1-1-1-2-2-2-2111111111111-2-2-20011001100000000002-1-1000
χ1922222-1-222-222-1-12-1-1-2-1-1-1-2-1112-1-1-12-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i322-200-1-1001100000000000−i3i3000
χ2022222-1-222-222-1-12-1-1-2-1-1-1-2-1112-1-1-12-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-22001100-1-100000000000i3−i3000
χ2122222-1-222-222-1-12-1-1-2-1-1-1-2-1112-1-1-12-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i322-200-1-1001100000000000i3−i3000
χ2222222-1-222-222-1-12-1-1-2-1-1-1-2-1112-1-1-12-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-22001100-1-100000000000−i3i3000
χ232222-122222-1-122-12-12-1-1-1-1222-1-1-12-1-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100022002200-1-1-1-1000000000-1-10
χ242222-122222-1-122-12-12-1-1-1-1222-1-1-12-1-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1000-2-200-2-2001111000000000110
χ252222-122222-1-122-12-12-1-1-1-1222-1-1-12-1-1-1-1-2-2-12-1-1-1-11111-2-21111-2-211110002200-2-2001111000000000-1-10
χ262222-122222-1-122-12-12-1-1-1-1222-1-1-12-1-1-1-1-2-2-12-1-1-1-11111-2-21111-2-21111000-2-2002200-1-1-1-1000000000110
χ272222-12-2-2-2-2-1-122-12-12-1-1-11-2-2-2111-2111100-1211-1-133−3−30033−3−30033−3−30002-200000033−3−3000000000-110
χ282222-12-2-2-2-2-1-122-12-12-1-1-11-2-2-2111-2111100-1211-1-133−3−30033−3−30033−3−3000-22000000−3−3330000000001-10
χ292222-12-2-2-2-2-1-122-12-12-1-1-11-2-2-2111-2111100-1211-1-1−3−33300−3−33300−3−3330002-2000000−3−333000000000-110
χ302222-12-2-2-2-2-1-122-12-12-1-1-11-2-2-2111-2111100-1211-1-1−3−33300−3−33300−3−333000-2200000033−3−30000000001-10
χ3122-2-222-20022-2-22-2-2202-2-2-202-200000002−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000002i−2i22−2−2000000
χ3222-2-222-20022-2-22-2-2202-2-2-202-200000002−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000−2i2i−2−222000000
χ3322-2-222-20022-2-22-2-2202-2-2-202-200000002i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000002i−2i−2−222000000
χ3422-2-222-20022-2-22-2-2202-2-2-202-200000002i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000−2i2i22−2−2000000
χ352-2-222202-20-2-22-22-220-22-20200222-2-2-2-200000000000000000000000002-20002-2−i2i200−i2i2−i2i200−i2i2−i2i2000000
χ362-2-222202-20-2-22-22-220-22-20200222-2-2-2-200000000000000000000000002-20002-2i2−i200i2−i2i2−i200i2−i2i2−i2000000
χ372-2-222202-20-2-22-22-220-22-20200222-2-2-2-20000000000000000000000000-22000-22−i2i200−i2i2−i2i200i2−i2i2−i2000000
χ382-2-222202-20-2-22-22-220-22-20200222-2-2-2-20000000000000000000000000-22000-22i2−i200i2−i2i2−i200−i2i2−i2i2000000
χ3944444-24-4-4444-2-24-2-2-4-2-2-242-2-2-4222-422400-42-2-2220000000000000000000000000000000000000000000
χ4044444-2-4-4-4-444-2-24-2-24-2-2-2-4222-4222-422-4004-222-2-20000000000000000000000000000000000000000000
χ414444-244-4-44-2-244-24-2-4-2-2-2-2-444222-4222-2002-4-2-2220000000000000000000000000000000000000000000
χ424444-24-444-4-2-244-24-2-4-2-2-224-4-4-2-2-24-2-2-22002-422220000000000000000000000000000000000000000000
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
χ454444-2-24-4-44-2-2-2-2-2-21-4111-22-2-22-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000
χ464444-2-24-4-44-2-2-2-2-2-21-4111-22-2-22-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000
χ474444-2-2-444-4-2-2-2-2-2-21-41112-222-211-2-21120022-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000000
χ484444-2-2-444-4-2-2-2-2-2-21-41112-222-211-2-21120022-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000000
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
χ5144-4-444400-44-4-44-4-4404-4-440-440000000-40000-44000000000000000000000000000000000000000000000
χ5244-4-44-2400-44-42-2-42-20-222402-20000000-400002-20000006−66−66−6−66−66−66000000000000000000000000000
χ5344-4-44-2400-44-42-2-42-20-222402-20000000-400002-2000000−66−66−666−66−66−6000000000000000000000000000
χ5444-4-44-2-40044-42-2-42-20-222-40-2200000004−2i22i200-2200−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000000
χ5544-4-44-2-40044-42-2-42-20-222-40-22000000042i2−2i200-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000000
χ5644-4-4-24400-4-22-442-4-20-222-20-440000000200002-200i6−i6−i6i600i6−i6−i6i600i6−i6−i6i6000000000000000000000000000
χ5744-4-4-24400-4-22-442-4-20-222-20-440000000200002-200−i6i6i6−i600−i6i6i6−i600−i6i6i6−i6000000000000000000000000000
χ5844-4-4-24-4004-22-442-4-20-222204-40000000-2−2i22i200-2200i2−i2i2−i2−2i22i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000000
χ5944-4-4-24-4004-22-442-4-20-222204-40000000-22i2−2i200-2200−i2i2−i2i22i2−2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000000
χ6044-4-4-2-2400-4-222-222101-1-1-202-203i−3i003i−3i20000-113i−3ii6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ6144-4-4-2-2400-4-222-222101-1-1-202-203i−3i003i−3i20000-113i−3i−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ6244-4-4-2-2400-4-222-222101-1-1-202-20−3i3i00−3i3i20000-11−3i3ii6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ6344-4-4-2-2400-4-222-222101-1-1-202-20−3i3i00−3i3i20000-11−3i3i−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ6444-4-4-2-2-4004-222-222101-1-120-2203i−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+2ζ23000000000000000000000000000
χ6544-4-4-2-2-4004-222-222101-1-120-2203i−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+ζ13−2ζ23000000000000000000000000000
χ6644-4-4-2-2-4004-222-222101-1-120-220−3i3i00−3i3i-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−ζ23000000000000000000000000000
χ6744-4-4-2-2-4004-222-222101-1-120-220−3i3i00−3i3i-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+ζ23000000000000000000000000000
χ684-44-4440000-44-4-4-4440-4-44000000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ694-44-4440000-44-4-4-4440-4-4400000000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ704-4-44440-440-4-44-44-440-44-40-400-4-4-444440000000000000000000000000000000000000000000000000000
χ714-4-444-204-40-4-4-2242-202-220-2004-2-22-42200000000000000000000000004-4000-2200000000000000000000
χ724-4-444-204-40-4-4-2242-202-220-2004-2-22-4220000000000000000000000000-440002-200000000000000000000
χ734-4-444-20-440-4-4-2242-202-220200-422-24-2-2000000000000000000000000000000000023−230000000000000000
χ744-4-444-20-440-4-4-2242-202-220200-422-24-2-20000000000000000000000000000000000−23230000000000000000
χ754-4-44-2404-40224-4-2-4-202-220400-2-2-2-422200000000000000000000000000000000−2i22i200i2−i2i2−i2000000000000
χ764-4-44-2404-40224-4-2-4-202-220400-2-2-2-4222000000000000000000000000000000002i2−2i200−i2i2−i2i2000000000000
χ774-4-44-240-440224-4-2-4-202-220-4002224-2-2-2000000000000000000000000000000000000i6−i6−i6i6000000000000
χ784-4-44-240-440224-4-2-4-202-220-4002224-2-2-2000000000000000000000000000000000000−i6i6i6−i6000000000000
χ798-88-88-40000-8844-8-4-4044-4000000000000000000000000000000000000000000000000000000000000000
χ808-88-8-4800004-4-8-848-4044-4000000000000000000000000000000000000000000000000000000000000000
χ818-88-8-4-400004-4444-420-2-22000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000
χ828-88-8-4-400004-4444-420-2-2200000−6i6i006i−6i0000000000000000000000000000000000000000000000000000
χ838-8-88-4-408-8044-44-4420-22-20-400-42244-2-20000000000000000000000000000000000000000000000000000
χ848-8-88-4-40-88044-44-4420-22-204004-2-2-4-4220000000000000000000000000000000000000000000000000000

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