Finite Group Databasebeta

← Group #10691996

Character table — Group #10691996

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222344444444666121212122224444444412121212121212126668888121212121212122424242424242424888888888888888888242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-11-1-1-1-11-1-1111111111-1-111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-11-1-1-1-11-1-1111111111-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ7111111111111111111111-1-11-1-1-1-11-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ8111111111111111111111-1-11-1-1-1-11-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911111-1-1-1-111-1-1111-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-111ii−i−i111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−ii−iii−i−i1-11-1
χ1011111-1-1-1-111-1-1111-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-111ii−i−i111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiii−iii−i−i-11-11
χ1111111-1-1-1-111-1-1111-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-111−i−iii111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−ii−i−iii-11-11
χ1211111-1-1-1-111-1-1111-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-111−i−iii111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−ii−i−iii1-11-1
χ1311111-1-1-1-111-1-1111-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1ii−i−i1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−ii−i−iii1-1-11
χ1411111-1-1-1-111-1-1111-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1ii−i−i1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−ii−i−iii-111-1
χ1511111-1-1-1-111-1-1111-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1−i−iii1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiii−iii−i−i-111-1
χ1611111-1-1-1-111-1-1111-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1−i−iii1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−ii−iii−i−i1-1-11
χ1722222222222-2-22222222-222-222-2-2-2-2-222-2-2-2-222-2220000-2-2-222-2-20000000000000000000000000000000000
χ1822222222222-2-22222222-2-2-2-2-2-222-22222-2-2-2-222-2-2-20000-222-2-2220000000000000000000000000000000000
χ192222222-2-2-2-2222222222-200-20000200-2-22222-2-2-2000000-2000000000000000000000022-2-222-2-20000000000
χ202222222-2-2-2-2222222222-200-20000200-2-22222-2-2-2000000-20000000000000000000000-2-222-2-2220000000000
χ212222222-2-2-2-2-2-2222222220020000-200-2-2-2-2-2-2-2-220000002000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ222222222-2-2-2-2-2-2222222220020000-200-2-2-2-2-2-2-2-22000000200000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2322222-2-222-2-222222-2-2-2-2-20020000-200-2-2-2-22222-200000020000000000000022-2-2-2-222000000000000000000
χ2422222-2-222-2-222222-2-2-2-2-20020000-200-2-2-2-22222-2000000200000000000000-2-22222-2-2000000000000000000
χ2522222-2-222-2-2-2-2222-2-2-2-2200-20000200-2-222-2-2222000000-200000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ2622222-2-222-2-2-2-2222-2-2-2-2200-20000200-2-222-2-2222000000-20000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ2722222-2-2-2-22222222-2-2-2-2222-2-2-222-2-2-222-2-222-2-22220000-2-2-2-2-2220000000000000000000000000000000000
χ2822222-2-2-2-22222222-2-2-2-22-2-2-222-2-2-22222-2-222-2-22-2-20000-22222-2-20000000000000000000000000000000000
χ292222-122222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ302222-122222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ312222-122222222-1-1-1-1-1-1-12-2-22-2-2-2-22-2-2-1-1-1-1-1-1-1-1-1112222-1111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ322222-122222222-1-1-1-1-1-1-12-2-22-2-2-2-22-2-2-1-1-1-1-1-1-1-1-111-2-2-2-2-111111111111111000000000000000022-1-1-1-10000
χ332222-1222222-2-2-1-1-1-1-1-1-1-222-222-2-2-2-2-2-1-11111-1-11-1-10000111-1-111−i3−i3i3i3−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ342222-1222222-2-2-1-1-1-1-1-1-1-222-222-2-2-2-2-2-1-11111-1-11-1-10000111-1-111i3i3−i3−i3i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ352222-1222222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-222-222-1-11111-1-111100001-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ362222-1222222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-222-222-1-11111-1-111100001-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ372222-1-2-2-2-22222-1-1-11111222-2-2-222-2-2-2-1-111-1-111-1-1-1000011111-1-133−3−3−3−3330000000000000000003−3−330000
χ382222-1-2-2-2-22222-1-1-11111222-2-2-222-2-2-2-1-111-1-111-1-1-1000011111-1-1−3−33333−3−3000000000000000000−333−30000
χ392222-1-2-2-2-22222-1-1-111112-2-2-222-2-2-222-1-111-1-111-11100001-1-1-1-11133−3−3−3−333000000000000000000−333−30000
χ402222-1-2-2-2-22222-1-1-111112-2-2-222-2-2-222-1-111-1-111-11100001-1-1-1-111−3−33333−3−30000000000000000003−3−330000
χ412222-1-2-2-2-222-2-2-1-1-11111-2222-2-2-2-2222-1-1-1-111111-1-12i2i−2i−2i-1-1-11111−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ422222-1-2-2-2-222-2-2-1-1-11111-2222-2-2-2-2222-1-1-1-111111-1-1−2i−2i2i2i-1-1-11111iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ432222-1-2-2-2-222-2-2-1-1-11111-2-2-2222222-2-2-1-1-1-111111112i2i−2i−2i-111-1-1-1-1−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ442222-1-2-2-2-222-2-2-1-1-11111-2-2-2222222-2-2-1-1-1-11111111−2i−2i2i2i-111-1-1-1-1iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ4522-2-222i−2i2i−2i2-2002-2-22i2i−2i−2i0000002-202i−2i2-200002i−2i000000002i−2i002-2000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ4622-2-222i−2i2i−2i2-2002-2-22i2i−2i−2i0000002-202i−2i2-200002i−2i000000002i−2i002-200000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ4722-2-222i−2i2i−2i2-2002-2-22i2i−2i−2i000000-220−2i2i2-200002i−2i00000000−2i2i00-22000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ4822-2-222i−2i2i−2i2-2002-2-22i2i−2i−2i000000-220−2i2i2-200002i−2i00000000−2i2i00-2200000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ4922-2-222i−2i−2i2i-22002-2-22i2i−2i−2i02-202i−2i00000-220000−2i2i02-200000002i−2i00000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ5022-2-222i−2i−2i2i-22002-2-22i2i−2i−2i02-202i−2i00000-220000−2i2i02-200000002i−2i0000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ5122-2-222i−2i−2i2i-22002-2-22i2i−2i−2i0-220−2i2i00000-220000−2i2i0-220000000−2i2i00000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ5222-2-222i−2i−2i2i-22002-2-22i2i−2i−2i0-220−2i2i00000-220000−2i2i0-220000000−2i2i0000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ5322-2-22−2i2i2i−2i-22002-2-2−2i−2i2i2i02-20−2i2i00000-2200002i−2i02-20000000−2i2i00000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ5422-2-22−2i2i2i−2i-22002-2-2−2i−2i2i2i02-20−2i2i00000-2200002i−2i02-20000000−2i2i0000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ5522-2-22−2i2i2i−2i-22002-2-2−2i−2i2i2i0-2202i−2i00000-2200002i−2i0-2200000002i−2i00000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ5622-2-22−2i2i2i−2i-22002-2-2−2i−2i2i2i0-2202i−2i00000-2200002i−2i0-2200000002i−2i0000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ5722-2-22−2i2i−2i2i2-2002-2-2−2i−2i2i2i0000002-20−2i2i2-20000−2i2i00000000−2i2i002-2000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ5822-2-22−2i2i−2i2i2-2002-2-2−2i−2i2i2i0000002-20−2i2i2-20000−2i2i00000000−2i2i002-200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ5922-2-22−2i2i−2i2i2-2002-2-2−2i−2i2i2i000000-2202i−2i2-20000−2i2i000000002i−2i00-22000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ6022-2-22−2i2i−2i2i2-2002-2-2−2i−2i2i2i000000-2202i−2i2-20000−2i2i000000002i−2i00-2200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ614444-244-4-4-4-444-2-2-2-2-2-2-2-400-4000040022-2-2-2-222200000020000000000000000000000000000000000000000
χ624444-244-4-4-4-4-4-4-2-2-2-2-2-2-240040000-40022222222-2000000-20000000000000000000000000000000000000000
χ634444-2-4-444-4-444-2-2-22222-40040000-4002222-2-2-2-22000000-20000000000000000000000000000000000000000
χ644444-2-4-444-4-4-4-4-2-2-22222400-4000040022-2-222-2-2-200000020000000000000000000000000000000000000000
χ6544-4-4-24i−4i4i−4i4-400-222−2i−2i2i2i0000004-404i−4i-220000−2i2i00000000−2i2i00-220000000000000000000000000000000000
χ6644-4-4-24i−4i4i−4i4-400-222−2i−2i2i2i000000-440−4i4i-220000−2i2i000000002i−2i002-20000000000000000000000000000000000
χ6744-4-4-24i−4i−4i4i-4400-222−2i−2i2i2i04-404i−4i000002-200002i−2i0-220000000−2i2i000000000000000000000000000000000000
χ6844-4-4-24i−4i−4i4i-4400-222−2i−2i2i2i0-440−4i4i000002-200002i−2i02-200000002i−2i000000000000000000000000000000000000
χ6944-4-4-2−4i4i4i−4i-4400-2222i2i−2i−2i04-40−4i4i000002-20000−2i2i0-2200000002i−2i000000000000000000000000000000000000
χ7044-4-4-2−4i4i4i−4i-4400-2222i2i−2i−2i0-4404i−4i000002-20000−2i2i02-20000000−2i2i000000000000000000000000000000000000
χ7144-4-4-2−4i4i−4i4i4-400-2222i2i−2i−2i0000004-40−4i4i-2200002i−2i000000002i−2i00-220000000000000000000000000000000000
χ7244-4-4-2−4i4i−4i4i4-400-2222i2i−2i−2i000000-4404i−4i-2200002i−2i00000000−2i2i002-20000000000000000000000000000000000
χ734-44-440000004i−4i-44-400000000000000000004i−4i000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ744-44-440000004i−4i-44-400000000000000000004i−4i00000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ754-44-44000000−4i4i-44-40000000000000000000−4i4i00000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ764-44-44000000−4i4i-44-40000000000000000000−4i4i000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ774-44-4-20000004i−4i2-22−2i32i3−2i32i3000000000000023−23−2i2i000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ2300000000000000000000000000
χ784-44-4-20000004i−4i2-22−2i32i3−2i32i3000000000000023−23−2i2i00000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ2300000000000000000000000000
χ794-44-4-20000004i−4i2-222i3−2i32i3−2i30000000000000−2323−2i2i000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ2300000000000000000000000000
χ804-44-4-20000004i−4i2-222i3−2i32i3−2i30000000000000−2323−2i2i00000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ2300000000000000000000000000
χ814-44-4-2000000−4i4i2-22−2i32i3−2i32i30000000000000−23232i−2i00000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ2300000000000000000000000000
χ824-44-4-2000000−4i4i2-22−2i32i3−2i32i30000000000000−23232i−2i000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ2300000000000000000000000000
χ834-44-4-2000000−4i4i2-222i3−2i32i3−2i3000000000000023−232i−2i00000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ2300000000000000000000000000
χ844-44-4-2000000−4i4i2-222i3−2i32i3−2i3000000000000023−232i−2i000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ2300000000000000000000000000
χ858-8-88800000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-40000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-8-88-40000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000

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