Finite Group Databasebeta

← Group #11781972

Character table — Group #11781972

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222244444444444444444888888888888888888888888242424242424242424242424363636364848484848487272
order1222334444666666346661212121212121212121212128812121212121224242424242424242424242424242424448812121212242424248888441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1111-1-1-1-1
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
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-11111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ92222222-2-222222222-2222-2-2-222222222-200-2-2-2-2-2-200000000000000002-20022-2-20000000000000000
χ102222222-2-222222222-2222-2-2-222222222-200-2-2-2-2-2-20000000000000000-2200-2-2220000000000000000
χ11222222-222-22222222-2222222-2-2-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000022-2-200000000
χ12222222-222-22222222-2222222-2-2-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000-2-22200000000
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
χ1522222-1222222-1-12-1-12-1-1-12-1-12-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12200-1-1-1-1000000002000-1-100
χ1622222-1222222-1-12-1-12-1-1-12-1-12-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200111100000000-20001100
χ1722222-1222222-1-12-1-12-1-1-12-1-12-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-21111111111112200-1-1-1-100000000-20001100
χ1822222-1222222-1-12-1-12-1-1-12-1-12-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-2111111111111-2-2001111000000002000-1-100
χ1922222-12-2-2222-1-12-1-1-2-1-1-1-2112-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i32-200-1-111000000000000−i3i300
χ2022222-12-2-2222-1-12-1-1-2-1-1-1-2112-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-220011-1-1000000000000i3−i300
χ2122222-12-2-2222-1-12-1-1-2-1-1-1-2112-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i32-200-1-111000000000000i3−i300
χ2222222-12-2-2222-1-12-1-1-2-1-1-1-2112-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-220011-1-1000000000000−i3i300
χ232222-122222-1-122-12-12-1-1-1-122-12-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100220000-1-1-1-1000002-1-10000
χ242222-122222-1-122-12-12-1-1-1-122-12-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100-2-20000111100000-2110000
χ252222-122222-1-122-12-12-1-1-1-122-12-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-2111100220000-1-1-1-100000-2110000
χ262222-122222-1-122-12-12-1-1-1-122-12-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-2111100-2-200001111000002-1-10000
χ272222-12-2-2-2-2-1-122-12-12-1-1-11-2-21-2111-211100-1211-1-133−3−30033−3−30033−3−3002i−2i0000−i−iii000000−i3i30000
χ282222-12-2-2-2-2-1-122-12-12-1-1-11-2-21-2111-211100-1211-1-133−3−30033−3−30033−3−300−2i2i0000ii−i−i000000i3−i30000
χ292222-12-2-2-2-2-1-122-12-12-1-1-11-2-21-2111-211100-1211-1-1−3−33300−3−33300−3−333002i−2i0000−i−iii000000i3−i30000
χ302222-12-2-2-2-2-1-122-12-12-1-1-11-2-21-2111-211100-1211-1-1−3−33300−3−33300−3−33300−2i2i0000ii−i−i000000−i3i30000
χ3122-2-22202-202-22-2-2-2202-2-222-200000000-22−2002-2002−22−22−22−22−22−22−22−20000000000002-2000000002−2
χ3222-2-22202-202-22-2-2-2202-2-222-200000000-22−2002-2002−22−22−22−22−22−22−22−2000000000000-2200000000−22
χ3322-2-22202-202-22-2-2-2202-2-222-200000000-2−22002-200−22−22−22−22−22−22−22−220000000000002-200000000−22
χ3422-2-22202-202-22-2-2-2202-2-222-200000000-2−22002-200−22−22−22−22−22−22−22−22000000000000-22000000002−2
χ3544444-2-444-444-2-24-2-2-4-2-2-24-2-2-4222-4222400-42-2-2220000000000000000000000000000000000000000
χ3644444-2-4-4-4-444-2-24-2-24-2-2-2-422-4222-4222-4004-222-2-20000000000000000000000000000000000000000
χ374444-244-4-44-2-244-24-2-4-2-2-22-4-4-24-2-2-24-2-22002-422220000000000000000000000000000000000000000
χ384444-24-444-4-2-244-24-2-4-2-2-2-2442-4222-422-2002-4-2-2220000000000000000000000000000000000000000
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
χ414444-2-24-4-44-2-2-2-2-2-21-4111222-2-211-2-21120022-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000
χ424444-2-24-4-44-2-2-2-2-2-21-4111222-2-211-2-21120022-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000
χ434444-2-2-444-4-2-2-2-2-2-21-4111-2-2-222-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000
χ444444-2-2-444-4-2-2-2-2-2-21-4111-2-2-222-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000
χ454444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1112323−23−2300−3−33300−3−333000000000000000000000000
χ464444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-111−23−2323230033−3−30033−3−3000000000000000000000000
χ4744-4-4440-4404-44-4-4-4404-4-4-4-440000000040000-44000000000000000000000000000000000000000000
χ4844-4-44-204-404-4-22-42-20-2224-2200000000-422−2200-220022−2222−22−22−22−22−22−22−22000000000000000000000000
χ4944-4-44-204-404-4-22-42-20-2224-2200000000-4−222200-2200−2222−22222−22−22−22−22−22−2000000000000000000000000
χ5044-4-44-20-4404-4-22-42-20-222-42-200000000400002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000
χ5144-4-44-20-4404-4-22-42-20-222-42-200000000400002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000
χ5244-4-4-2404-40-224-42-4-20-222-24-400000000222−2200-2200−22−2222−22−22−2222−22−22−22000000000000000000000000
χ5344-4-4-2404-40-224-42-4-20-222-24-4000000002−222200-22002−22−2−22222−22−2−22222−22−2000000000000000000000000
χ5444-4-4-240-440-224-42-4-20-2222-4400000000-200002-2006−6−66006−6−66006−6−66000000000000000000000000
χ5544-4-4-240-440-224-42-4-20-2222-4400000000-200002-200−666−600−666−600−666−6000000000000000000000000
χ5644-4-4-2-204-40-22-2222101-1-1-2-22003i−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+ζ23000000000000000000000000
χ5744-4-4-2-204-40-22-2222101-1-1-2-22003i−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−ζ23000000000000000000000000
χ5844-4-4-2-204-40-22-2222101-1-1-2-2200−3i3i00−3i3i222−22001-1−3i3i−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−ζ13−2ζ23000000000000000000000000
χ5944-4-4-2-204-40-22-2222101-1-1-2-2200−3i3i00−3i3i2−2222001-1−3i3i2−22−22−2−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+2ζ23000000000000000000000000
χ6044-4-4-2-20-440-22-2222101-1-122-2003i−3i003i−3i-20000-11−3i3i6−6−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ6144-4-4-2-20-440-22-2222101-1-122-2003i−3i003i−3i-20000-11−3i3i−666−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ6244-4-4-2-20-440-22-2222101-1-122-200−3i3i00−3i3i-20000-113i−3i6−6−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ6344-4-4-2-20-440-22-2222101-1-122-200−3i3i00−3i3i-20000-113i−3i−666−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ644-44-4440000-44-44-4-440-44-40000000000000000000000000000000000000000000000000022−2200000000
χ654-44-4440000-44-44-4-440-44-400000000000000000000000000000000000000000000000000−222200000000
χ664-4-4444400-4-4-4-4-44440-4-44000-4-4-4-444440000000000000000000000000000000000000000000000000
χ674-4-4444-4004-4-4-4-44440-4-440004444-4-4-4-40000000000000000000000000000000000000000000000000
χ684-4-444-2400-4-4-4224-2-2022-2000-42224-2-2-20000000000000000000000000000000−2i32i30000000000000000
χ694-4-444-2400-4-4-4224-2-2022-2000-42224-2-2-200000000000000000000000000000002i3−2i30000000000000000
χ704-4-444-2-4004-4-4224-2-2022-20004-2-2-2-42220000000000000000000000000000023−23000000000000000000
χ714-4-444-2-4004-4-4224-2-2022-20004-2-2-2-422200000000000000000000000000000−2323000000000000000000
χ724-4-44-24400-422-4-4-24-2022-20002-422-24-2-2000000000000000000000000000000000i6−i6i6−i6000000000000
χ734-4-44-24400-422-4-4-24-2022-20002-422-24-2-2000000000000000000000000000000000−i6i6−i6i6000000000000
χ744-4-44-24-400422-4-4-24-2022-2000-24-2-22-4220000000000000000000000000000000006−6−66000000000000
χ754-4-44-24-400422-4-4-24-2022-2000-24-2-22-422000000000000000000000000000000000−666−6000000000000
χ768-88-88-40000-884-4-84-404-44000000000000000000000000000000000000000000000000000000000000
χ778-88-8-4800004-4-884-8-404-44000000000000000000000000000000000000000000000000000000000000
χ788-88-8-4-400004-44-44420-22-2000006i−6i00−6i6i0000000000000000000000000000000000000000000000000
χ798-88-8-4-400004-44-44420-22-200000−6i6i006i−6i0000000000000000000000000000000000000000000000000
χ808-8-88-4-4800-84444-4-420-2-2200044-2-2-4-4220000000000000000000000000000000000000000000000000
χ818-8-88-4-4-80084444-4-420-2-22000-4-42244-2-20000000000000000000000000000000000000000000000000

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