Finite Group Databasebeta

← Group #10848584

Character table — Group #10848584

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222222222222222444444444448888888888888888888888888888881212121216161616242424242424242424244848
order1222222222344666666644466661212121222444444444466661212121212121212121212121212444412121212222444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-11-1-1-1-1-1-111
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1111111-1-1
χ51111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ61111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-11-1-11-1-11111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ911111111111-1-11111111-1-1-11111-1-1-1-1111-11-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-11-111-1-11-1
χ1011111111111-1-11111111-1-1-11111-1-1-1-1111-11-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-111-11-1-111-11
χ1111111111111-1-11111111-1-1-11111-1-1-1-111-11-11-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-11-11-1-11-1-11-1-1111-1
χ1211111111111-1-11111111-1-1-11111-1-1-1-111-11-11-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1111-111-111-1-1-11
χ1311111111111-1-11111111-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-111111111-1-111111-11-1-11-1-11-1-1-111-11
χ1411111111111-1-11111111-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-11-11-111-1111-1-11-1
χ1511111111111-1-11111111-1-1-11111-1-1-1-1-1-1-11-111111-1-1-1-1-1-11111-1-1-1-11111-1-11111-11-11-1-11-1-1111-1-1-11
χ1611111111111-1-11111111-1-1-11111-1-1-1-1-1-1-11-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1111-111-1-1-1111-1
χ172222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000000
χ182222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-100001111000000000000
χ192222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-21111111111111111-1-10000-1-1-1-1000000000000
χ202222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-1-1-1-1-1-1-11111-1-100001111000000000000
χ212222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-1-1-1-11111222-22-2-2-222-2-2-1-1-1-1-1-1-1-111111111110000-11-11000000000000
χ222222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-1-1-1-1111122-22-22-2-2-2-222-1-1-1-11111-1-1-1-111111100001-11-1000000000000
χ232222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-22-22-222-2-22211111111-1-1-1-1-1-1-1-1110000-11-11000000000000
χ242222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-2-22-222222-2-21111-1-1-1-11111-1-1-1-11100001-11-1000000000000
χ2522222-2-2-2-22222-2-2-2-22222-2-222-2-222-2-200000000000000000000000000002-222-2-20000-200200000000
χ2622222-2-2-2-22222-2-2-2-22222-2-222-2-222-2-200000000000000000000000000002-2-2-2220000200-200000000
χ2722222-2-2-2-222-2-2-2-2-2-2222-22222-2-2-2-2220000000000000000000000000000-2222-2-20000200-200000000
χ2822222-2-2-2-222-2-2-2-2-2-2222-22222-2-2-2-2220000000000000000000000000000-22-2-2220000-200200000000
χ292222-222-2-2-22222222222-22-2-2-2-2-22222002-2-220000000000000000000000-2-200002-2-22000000000000
χ302222-222-2-2-22222222222-22-2-2-2-2-2222200-222-20000000000000000000000-2-20000-222-2000000000000
χ312222-222-2-2-22-2-222222222-22-2-2-2-2-2-2-2-20022-2-2000000000000000000000022000022-2-2000000000000
χ322222-222-2-2-22-2-222222222-22-2-2-2-2-2-2-2-200-2-2220000000000000000000000220000-2-222000000000000
χ332222-222-2-2-2-122-1-1-1-1-1-1-1-22-21111-1-1-1-1002-2-22000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3110000-111-1000000000000
χ342222-222-2-2-2-122-1-1-1-1-1-1-1-22-21111-1-1-1-1002-2-22000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3110000-111-1000000000000
χ352222-222-2-2-2-122-1-1-1-1-1-1-1-22-21111-1-1-1-100-222-2000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i31100001-1-11000000000000
χ362222-222-2-2-2-122-1-1-1-1-1-1-1-22-21111-1-1-1-100-222-2000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i31100001-1-11000000000000
χ372222-222-2-2-2-1-2-2-1-1-1-1-1-1-12-22111111110022-2-2000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-1-10000-1-111000000000000
χ382222-222-2-2-2-1-2-2-1-1-1-1-1-1-12-22111111110022-2-2000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-1-10000-1-111000000000000
χ392222-222-2-2-2-1-2-2-1-1-1-1-1-1-12-221111111100-2-222000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-1000011-1-1000000000000
χ402222-222-2-2-2-1-2-2-1-1-1-1-1-1-12-221111111100-2-222000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-1000011-1-1000000000000
χ412222-2-2-222-2222-2-2-2-2222-2-22-2-22222-2-20000000000000000000000000000-220000000002-20-22000000
χ422222-2-2-222-2222-2-2-2-2222-2-22-2-22222-2-20000000000000000000000000000-22000000000-2202-2000000
χ432222-2-2-222-22-2-2-2-2-2-222222-2-2-222-2-22200000000000000000000000000002-2000000000220-2-2000000
χ442222-2-2-222-22-2-2-2-2-2-222222-2-2-222-2-22200000000000000000000000000002-2000000000-2-2022000000
χ452-2-2222-22-2-220022-2-22-2-20002-22-2000000000000002i−2i000000002i−2i2i−2i0000002i−2i2i−2i0000000000002-200
χ462-2-2222-22-2-220022-2-22-2-20002-22-2000000000000002i−2i000000002i−2i2i−2i000000−2i2i−2i2i000000000000-2200
χ472-2-2222-22-2-220022-2-22-2-20002-22-200000000000000−2i2i00000000−2i2i−2i2i0000002i−2i2i−2i000000000000-2200
χ482-2-2222-22-2-220022-2-22-2-20002-22-200000000000000−2i2i00000000−2i2i−2i2i000000−2i2i−2i2i0000000000002-200
χ492-2-222-22-22-2200-2-2222-2-20002-2-220000000000002i−2i0000002i−2i2i−2i00000000002i−2i−2i2i00000000002-20000
χ502-2-222-22-22-2200-2-2222-2-20002-2-220000000000002i−2i0000002i−2i2i−2i0000000000−2i2i2i−2i0000000000-220000
χ512-2-222-22-22-2200-2-2222-2-20002-2-22000000000000−2i2i000000−2i2i−2i2i00000000002i−2i−2i2i0000000000-220000
χ522-2-222-22-22-2200-2-2222-2-20002-2-22000000000000−2i2i000000−2i2i−2i2i0000000000−2i2i2i−2i00000000002-20000
χ5344444-4-4-4-44-2442222-2-2-24-4-4-2-222-2-2220000000000000000000000000000-2200000000000000000000
χ5444444-4-4-4-44-2-4-42222-2-2-2-444-2-22222-2-200000000000000000000000000002-200000000000000000000
χ554444-4-4-444-4-2442222-2-2-2-4-4422-2-2-2-22200000000000000000000000000002-200000000000000000000
χ564444-4-4-444-4-2-4-42222-2-2-244-422-2-222-2-20000000000000000000000000000-2200000000000000000000
χ5744-4-400000044i−4i0000-44-400000004i−4i002-200002i−2i00002-22-2000000002i−2i2i−2i0000000000000000000000
χ5844-4-400000044i−4i0000-44-400000004i−4i00-220000−2i2i0000-22-2200000000−2i2i−2i2i0000000000000000000000
χ5944-4-40000004−4i4i0000-44-40000000−4i4i002-20000−2i2i00002-22-200000000−2i2i−2i2i0000000000000000000000
χ6044-4-40000004−4i4i0000-44-40000000−4i4i00-2200002i−2i0000-22-22000000002i−2i2i−2i0000000000000000000000
χ6144-4-4000000-24i−4i−2i32i3−2i32i32-220000000−2i2i23−232-200002i−2i0000−1−i31+i3−1+i31−i3000000002ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ6244-4-4000000-24i−4i−2i32i3−2i32i32-220000000−2i2i23−23-220000−2i2i00001+i3−1−i31−i3−1+i300000000−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ6344-4-4000000-24i−4i2i3−2i32i3−2i32-220000000−2i2i−23232-200002i−2i0000−1+i31−i3−1−i31+i3000000002ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ6444-4-4000000-24i−4i2i3−2i32i3−2i32-220000000−2i2i−2323-220000−2i2i00001−i3−1+i31+i3−1−i300000000−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ6544-4-4000000-2−4i4i−2i32i3−2i32i32-2200000002i−2i−23232-20000−2i2i0000−1−i31+i3−1+i31−i300000000−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ6644-4-4000000-2−4i4i−2i32i3−2i32i32-2200000002i−2i−2323-2200002i−2i00001+i3−1−i31−i3−1+i3000000002ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ6744-4-4000000-2−4i4i2i3−2i32i3−2i32-2200000002i−2i23−232-20000−2i2i0000−1+i31−i3−1−i31+i300000000−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ6844-4-4000000-2−4i4i2i3−2i32i3−2i32-2200000002i−2i23−23-2200002i−2i00001−i3−1+i31+i3−1−i3000000002ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ694-4-4444-44-4-4-200-2-222-222000-22-22000000000000004i−4i00000000−2i2i−2i2i00000000000000000000000000
χ704-4-4444-44-4-4-200-2-222-222000-22-2200000000000000−4i4i000000002i−2i2i−2i00000000000000000000000000
χ714-4-444-44-44-4-20022-2-2-222000-222-20000000000004i−4i000000−2i2i−2i2i000000000000000000000000000000
χ724-4-444-44-44-4-20022-2-2-222000-222-2000000000000−4i4i0000002i−2i2i−2i000000000000000000000000000000
χ734-4-44-44-4-44440044-4-44-4-4000-44-44000000000000000000000000000000000000000000000000000000
χ744-4-44-44-4-444-200-2-222-2220002-22-200000000000000000000000023−23−232300000000000000000000000000
χ754-4-44-44-4-444-200-2-222-2220002-22-2000000000000000000000000−232323−2300000000000000000000000000
χ764-4-44-4-444-44400-4-4444-4-4000-444-4000000000000000000000000000000000000000000000000000000
χ774-4-44-4-444-44-20022-2-2-2220002-2-220000000000000000000023−23−2323000000000000000000000000000000
χ784-4-44-4-444-44-20022-2-2-2220002-2-2200000000000000000000−232323−23000000000000000000000000000000
χ798-88-80000008000000-8-880000000000000000000000000000000000000000000000000000000000000
χ808-88-8000000-400−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000
χ818-88-8000000-4004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.