Finite Group Databasebeta

← Group #11781219

Character table — Group #11781219

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222222222244444444444444444888888888888888888888888121212121212121218181818242424242424242436364848484848487272
order1222334444666666346661212121212121212121212128812121212121224242424242424242424242424242424444488888888121212122424242488441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-1-11111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ92222222-2-222222222-22222-2-2-22222222-200-2-2-2-2-2-2000000000000000022-2-20000000022-2-200000000000000
χ102222222-2-222222222-22222-2-2-22222222-200-2-2-2-2-2-20000000000000000-2-22200000000-2-22200000000000000
χ11222222-222-22222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-2000000000000000000000000222200000000-2-200000000
χ12222222-222-22222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-2000000000000000000000000-2-2-2-2000000002200000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000002i2i−2i−2i000000002i2i−2i−2i0000000000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-22200000000000000000000−2i−2i2i2i00000000−2i−2i2i2i0000000000
χ1522222-1222222-1-12-1-12-1-1-122-1-1-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-10000002000-1-100
χ1622222-1222222-1-12-1-12-1-1-122-1-1-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000001111000000-20001100
χ1722222-1222222-1-12-1-12-1-1-122-1-1-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-2111111111111222200000000-1-1-1-1000000-20001100
χ1822222-1222222-1-12-1-12-1-1-122-1-1-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-2111111111111-2-2-2-20000000011110000002000-1-100
χ1922222-12-2-2222-1-12-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i322-2-200000000-1-1110000000000−i3i300
χ2022222-12-2-2222-1-12-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-2220000000011-1-10000000000i3−i300
χ2122222-12-2-2222-1-12-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i322-2-200000000-1-1110000000000i3−i300
χ2222222-12-2-2222-1-12-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-2220000000011-1-10000000000−i3i300
χ232222-122222-1-122-12-12-1-1-1-1-1222-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000222200000000-1-1-1-10002-1-10000
χ242222-122222-1-122-12-12-1-1-1-1-1222-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-2-2-2000000001111000-2110000
χ252222-122222-1-122-12-12-1-1-1-1-1222-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-211110000222200000000-1-1-1-1000-2110000
χ262222-122222-1-122-12-12-1-1-1-1-1222-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-211110000-2-2-2-20000000011110002-1-10000
χ272222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2111-211100-1211-1-133−3−30033−3−30033−3−300002i2i−2i−2i00000000−i−iii0000−i3i30000
χ282222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2111-211100-1211-1-133−3−30033−3−30033−3−30000−2i−2i2i2i00000000ii−i−i0000i3−i30000
χ292222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2111-211100-1211-1-1−3−33300−3−33300−3−33300002i2i−2i−2i00000000−i−iii0000i3−i30000
χ302222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2111-211100-1211-1-1−3−33300−3−33300−3−3330000−2i−2i2i2i00000000ii−i−i0000−i3i30000
χ3122-2-22202-202-22-2-2-2202-2-2022-20000000-22−2002-2002−22−22−22−22−22−22−22−20000000022-2-200000000000000002−2
χ3222-2-22202-202-22-2-2-2202-2-2022-20000000-22−2002-2002−22−22−22−22−22−22−22−200000000-2-2220000000000000000−22
χ3322-2-22202-202-22-2-2-2202-2-2022-20000000-2−22002-200−22−22−22−22−22−22−22−220000000022-2-20000000000000000−22
χ3422-2-22202-202-22-2-2-2202-2-2022-20000000-2−22002-200−22−22−22−22−22−22−22−2200000000-2-22200000000000000002−2
χ352-22-222200-2-22-22-2-220-22-22000222-2-2-2-200000000000000000000000002-2002−22−22−22−22-2002−22−22−200000000
χ362-22-222200-2-22-22-2-220-22-22000222-2-2-2-200000000000000000000000002-200−22−22−22−222-200−22−22−2200000000
χ372-22-222200-2-22-22-2-220-22-22000222-2-2-2-20000000000000000000000000-22002−22−2−22−22-22002−22−2−2200000000
χ382-22-222200-2-22-22-2-220-22-22000222-2-2-2-20000000000000000000000000-2200−22−222−22−2-2200−22−222−200000000
χ392-22-222-2002-22-22-2-220-22-2-2000-2-2-222220000000000000000000000000002i−2i−i2i2i2−i22−22−2002i−2i−i2i2i2−i2−2200000000
χ402-22-222-2002-22-22-2-220-22-2-2000-2-2-222220000000000000000000000000002i−2ii2−i2−i2i2−22−22002i−2ii2−i2−i2i22−200000000
χ412-22-222-2002-22-22-2-220-22-2-2000-2-2-22222000000000000000000000000000−2i2i−i2i2i2−i2−22−2200−2i2i−i2i2i2−i22−200000000
χ422-22-222-2002-22-22-2-220-22-2-2000-2-2-22222000000000000000000000000000−2i2ii2−i2−i2i22−22−200−2i2ii2−i2−i2i2−2200000000
χ4344444-2-444-444-2-24-2-2-4-2-2-2-44-2-2222-4222400-42-2-2220000000000000000000000000000000000000000000000
χ4444444-2-4-4-4-444-2-24-2-24-2-2-2-4-422222-4222-4004-222-2-20000000000000000000000000000000000000000000000
χ454444-244-4-44-2-244-24-2-4-2-2-2-22-4-44-2-2-24-2-22002-422220000000000000000000000000000000000000000000000
χ464444-24-444-4-2-244-24-2-4-2-2-22-244-4222-422-2002-4-2-2220000000000000000000000000000000000000000000000
χ474444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-244-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000000
χ484444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-2-4-4-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000000
χ494444-2-24-4-44-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000000000
χ504444-2-24-4-44-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000000000
χ514444-2-2-444-4-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000000
χ524444-2-2-444-4-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000000
χ534444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1112323−23−2300−3−33300−3−333000000000000000000000000000000
χ544444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-111−23−2323230033−3−30033−3−3000000000000000000000000000000
χ5544-4-4440-4404-44-4-4-4404-4-40-4-44000000040000-44000000000000000000000000000000000000000000000000
χ5644-4-44-204-404-4-22-42-20-22204-220000000-422−2200-220022−2222−22−22−22−22−22−22−22000000000000000000000000000000
χ5744-4-44-204-404-4-22-42-20-22204-220000000-4−222200-2200−2222−22222−22−22−22−22−22−2000000000000000000000000000000
χ5844-4-44-20-4404-4-22-42-20-2220-42-20000000400002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ5944-4-44-20-4404-4-22-42-20-2220-42-20000000400002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ6044-4-4-2404-40-224-42-4-20-2220-24-40000000222−2200-2200−22−2222−22−22−2222−22−22−22000000000000000000000000000000
χ6144-4-4-2404-40-224-42-4-20-2220-24-400000002−222200-22002−22−2−22222−22−2−22222−22−2000000000000000000000000000000
χ6244-4-4-240-440-224-42-4-20-22202-440000000-200002-2006−6−66006−6−66006−6−66000000000000000000000000000000
χ6344-4-4-240-440-224-42-4-20-22202-440000000-200002-200−666−600−666−600−666−6000000000000000000000000000000
χ6444-4-4-2-204-40-22-2222101-1-10-2-2203i−3i003i−3i222−22001-13i−3i−22−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23000000000000000000000000000000
χ6544-4-4-2-204-40-22-2222101-1-10-2-2203i−3i003i−3i2−2222001-13i−3i2−22−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23000000000000000000000000000000
χ6644-4-4-2-204-40-22-2222101-1-10-2-220−3i3i00−3i3i222−22001-1−3i3i−22−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23000000000000000000000000000000
χ6744-4-4-2-204-40-22-2222101-1-10-2-220−3i3i00−3i3i2−2222001-1−3i3i2−22−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23000000000000000000000000000000
χ6844-4-4-2-20-440-22-2222101-1-1022-203i−3i003i−3i-20000-11−3i3i6−6−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ6944-4-4-2-20-440-22-2222101-1-1022-203i−3i003i−3i-20000-11−3i3i−666−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ7044-4-4-2-20-440-22-2222101-1-1022-20−3i3i00−3i3i-20000-113i−3i6−6−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ7144-4-4-2-20-440-22-2222101-1-1022-20−3i3i00−3i3i-20000-113i−3i−666−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ724-44-44-2400-4-442-2-42-202-224000-2-2-2-422200000000000000000000000004-40000000000-220000000000000000
χ734-44-44-2400-4-442-2-42-202-224000-2-2-2-42220000000000000000000000000-4400000000002-20000000000000000
χ744-44-44-2-4004-442-2-42-202-22-40002224-2-2-20000000000000000000000000004i−4i0000000000−2i2i00000000000000
χ754-44-44-2-4004-442-2-42-202-22-40002224-2-2-2000000000000000000000000000−4i4i00000000002i−2i00000000000000
χ764-44-4-24400-42-2-442-4-202-22-20004-2-22-4220000000000000000000000000000022−2222−2200000000−22−220000000000
χ774-44-4-24400-42-2-442-4-202-22-20004-2-22-42200000000000000000000000000000−2222−2222000000002−22−20000000000
χ784-44-4-24-40042-2-442-4-202-222000-422-24-2-200000000000000000000000000000−2i22i22i2−2i200000000i2−i2−i2i20000000000
χ794-44-4-24-40042-2-442-4-202-222000-422-24-2-2000000000000000000000000000002i2−2i2−2i22i200000000−i2i2i2−i20000000000
χ804-4-44440000-4-4-4-44440-4-440000000000000000000000000000000000000000000022−22−2222000000000000000000
χ814-4-44440000-4-4-4-44440-4-4400000000000000000000000000000000000000000000−222222−22000000000000000000
χ828-88-8-4-4800-84-44-44420-22-2-4000-42244-2-20000000000000000000000000000000000000000000000000000000
χ838-88-8-4-4-80084-44-44420-22-240004-2-2-4-4220000000000000000000000000000000000000000000000000000000
χ848-8-888-40000-8-8448-4-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ858-8-88-48000044-8-8-48-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-4-400004444-4-420-2-22000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000000
χ878-8-88-4-400004444-4-420-2-2200000−6i6i006i−6i0000000000000000000000000000000000000000000000000000000

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