Finite Group Databasebeta

← Group #10833355

Character table — Group #10833355

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order1222222234444446666666244444444466661212121212121212121212121212121212121212121212122244224424666612121212224444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111-1-1-11-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1111-111111-1-1
χ911111-1-1111-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111-11111-1-1-1-1-11-1-1-1111-1-11-1
χ1011111-1-1111-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-11-1111-1-1-111-11
χ1111111-1-1111-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-11111-1-111-1-111-1-1-11
χ1211111-1-1111-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-1111111-1-111-1-1111-1
χ1311111-1-1111-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-1-1-111-11-1-1-11-1-111-11
χ1411111-1-1111-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1111-1111-111-1-11-1
χ1511111-1-1111-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111111-1-1-11111-1-1-1-111-1-1-1-1111-1
χ1611111-1-1111-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-11111-1-111-1-11111-1-1-11
χ17222222222-2-2-2-2-2-222222222-2000000002222-2-2-2-2-2-2-2-200000000000000002-22-20000002-2002-200000000000000
χ18222222222-2-2-2-2-2-222222222-2000000002222-2-2-2-2-2-2-2-20000000000000000-22-22000000-2200-2200000000000000
χ1922222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ2022222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ2122222222-1222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122220000-2-2-1-111-1-111000000000000
χ2222222222-1222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-200002211-1-111-1-1000000000000
χ2322222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-2000000-11−i3i3-11−i3i3000000000000
χ2422222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-220000001-1i3−i31-1i3−i3000000000000
χ2522222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-2000000-11i3−i3-11i3−i3000000000000
χ2622222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-220000001-1−i3i31-1−i3i3000000000000
χ2722222-2-222-222-2-2-22222222-2200000000-2-2-2-2-2-2-2-2222200000000000000002-2-220000002-200-2200000000000000
χ2822222-2-222-222-2-2-22222222-2200000000-2-2-2-2-2-2-2-222220000000000000000-222-2000000-22002-200000000000000
χ2922222-2-22-12-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-11111-1-1-1-1-1-1-1-11111111122-2-200002-2-1-1-1-11111000000000000
χ3022222-2-22-12-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111111111-2-2220000-221111-1-1-1-1000000000000
χ3122222-2-22-12-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-1111111111111-1-1-1-1-1-1-1-122-2-20000-22-1-11111-1-1000000000000
χ3222222-2-22-12-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-2-22200002-211-1-1-1-111000000000000
χ3322222-2-22-1-222-2-2-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-22000000-11−i3i31-1i3−i3000000000000
χ3422222-2-22-1-222-2-2-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-222-20000001-1i3−i3-11−i3i3000000000000
χ3522222-2-22-1-222-2-2-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-22000000-11i3−i31-1−i3i3000000000000
χ3622222-2-22-1-222-2-2-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-222-20000001-1−i3i3-11i3−i3000000000000
χ372222-222-22222-2-222-2-22-2-22-2-20000000022-2-222-2-222-2-2000000000000000000000000000000000002-220-2000000
χ382222-222-22222-2-222-2-22-2-22-2-20000000022-2-222-2-222-2-200000000000000000000000000000000000-22-202000000
χ392222-222-22-2-2-222-22-2-22-2-22-220000000022-2-2-2-222-2-2220000000000000000000022-2-200000000002000-20000000
χ402222-222-22-2-2-222-22-2-22-2-22-220000000022-2-2-2-222-2-22200000000000000000000-2-2220000000000-200020000000
χ412222-2-2-2-222-2-2-2-222-2-22-2-222200000000-2-22222-2-2-2-2220000000000000000000000000000000000022-20-2000000
χ422222-2-2-2-222-2-2-2-222-2-22-2-222200000000-2-22222-2-2-2-22200000000000000000000000000000000000-2-2202000000
χ432222-2-2-2-22-22222-22-2-22-2-222-200000000-2-222-2-22222-2-20000000000000000000022-2-20000000000-200020000000
χ442222-2-2-2-22-22222-22-2-22-2-222-200000000-2-222-2-22222-2-200000000000000000000-2-22200000000002000-20000000
χ452-2-22200-222002-2-2-2222-2-2-20000002i2i−2i−2i00002-22-20000000000002i2i−2i−2i2i2i−2i−2i00002-22-20000000000000000002i−2i00
χ462-2-22200-222002-2-2-2222-2-2-20000002i2i−2i−2i00002-22-20000000000002i2i−2i−2i2i2i−2i−2i0000-22-22000000000000000000−2i2i00
χ472-2-22200-222002-2-2-2222-2-2-2000000−2i−2i2i2i00002-22-2000000000000−2i−2i2i2i−2i−2i2i2i00002-22-2000000000000000000−2i2i00
χ482-2-22200-222002-2-2-2222-2-2-2000000−2i−2i2i2i00002-22-2000000000000−2i−2i2i2i−2i−2i2i2i0000-22-220000000000000000002i−2i00
χ492-2-22-20022-2002-22-2-2-2222-20022-2-200000000-222-2000022-2-222-2-20000000000002-2-2200000000000000002-20000
χ502-2-22-20022-2002-22-2-2-2222-20022-2-200000000-222-2000022-2-222-2-2000000000000-222-20000000000000000-220000
χ512-2-22-20022-2002-22-2-2-2222-200-2-22200000000-222-20000-2-222-2-2220000000000002-2-220000000000000000-220000
χ522-2-22-20022-2002-22-2-2-2222-200-2-22200000000-222-20000-2-222-2-222000000000000-222-200000000000000002-20000
χ534444-444-4-2444-4-44-222-222-2-4-400000000-2-222-2-222-2-2220000000000000000000000000000000000000000000000
χ544444-444-4-2-4-4-444-4-222-222-2-4400000000-2-22222-2-222-2-20000000000000000000000000000000000000000000000
χ554444-4-4-4-4-24-4-4-4-44-222-222-2440000000022-2-2-2-22222-2-20000000000000000000000000000000000000000000000
χ564444-4-4-4-4-2-44444-4-222-222-24-40000000022-2-222-2-2-2-2220000000000000000000000000000000000000000000000
χ5744-4-40000404i−4i000400-400-4002-22-22i−2i2i−2i000000004i−4i002-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ5844-4-40000404i−4i000400-400-400-22-22−2i2i−2i2i000000004i−4i00-22-22-22-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ5944-4-4000040−4i4i000400-400-4002-22-2−2i2i−2i2i00000000−4i4i002-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ6044-4-4000040−4i4i000400-400-400-22-222i−2i2i−2i00000000−4i4i00-22-22-22-222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ6144-4-40000-204i−4i000-2−2i32i32−2i32i32002-22-22i−2i2i−2i00000000−2i2i23−23−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i32ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11000000000000000000000000000000
χ6244-4-40000-204i−4i000-2−2i32i32−2i32i3200-22-22−2i2i−2i2i00000000−2i2i23−231+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11000000000000000000000000000000
χ6344-4-40000-204i−4i000-22i3−2i322i3−2i32002-22-22i−2i2i−2i00000000−2i2i−2323−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i32ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ7000000000000000000000000000000
χ6444-4-40000-204i−4i000-22i3−2i322i3−2i3200-22-22−2i2i−2i2i00000000−2i2i−23231−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7000000000000000000000000000000
χ6544-4-40000-20−4i4i000-2−2i32i32−2i32i32002-22-2−2i2i−2i2i000000002i−2i−2323−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11000000000000000000000000000000
χ6644-4-40000-20−4i4i000-2−2i32i32−2i32i3200-22-222i−2i2i−2i000000002i−2i−23231+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i32ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11000000000000000000000000000000
χ6744-4-40000-20−4i4i000-22i3−2i322i3−2i32002-22-2−2i2i−2i2i000000002i−2i23−23−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7000000000000000000000000000000
χ6844-4-40000-20−4i4i000-22i3−2i322i3−2i3200-22-222i−2i2i−2i000000002i−2i23−231−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i32ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ7000000000000000000000000000000
χ694-44-404-404000000-400-4004002-2-222-2-224-400000000002-2-222-2-222-2-222-2-22000000000000000000000000000000
χ704-44-404-404000000-400-400400-222-2-222-24-40000000000-222-2-222-2-222-2-222-2000000000000000000000000000000
χ714-44-404-40-20000002−2i32i322i3−2i3-2002-2-222-2-22-22−2i32i300000000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000000000000000000000
χ724-44-404-40-20000002−2i32i322i3−2i3-200-222-2-222-2-22−2i32i3000000001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3000000000000000000000000000000
χ734-44-404-40-200000022i3−2i32−2i32i3-2002-2-222-2-22-222i3−2i300000000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3000000000000000000000000000000
χ744-44-404-40-200000022i3−2i32−2i32i3-200-222-2-222-2-222i3−2i3000000001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3000000000000000000000000000000
χ754-44-40-4404000000-400-4004002-2-22-222-2-4400000000002-2-222-2-22-222-2-222-2000000000000000000000000000000
χ764-44-40-4404000000-400-400400-222-22-2-22-440000000000-222-2-222-22-2-222-2-22000000000000000000000000000000
χ774-44-40-440-20000002−2i32i322i3−2i3-2002-2-22-222-22-22i3−2i300000000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3000000000000000000000000000000
χ784-44-40-440-20000002−2i32i322i3−2i3-200-222-22-2-222-22i3−2i3000000001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000000000000000000000
χ794-44-40-440-200000022i3−2i32−2i32i3-2002-2-22-222-22-2−2i32i300000000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3000000000000000000000000000000
χ804-44-40-440-200000022i3−2i32−2i32i3-200-222-22-2-222-2−2i32i3000000001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3000000000000000000000000000000
χ814-4-44400-44-400-444-4444-4-4-400000000000000-44-4400000000000000000000000000000000000000000000000000
χ824-4-44400-4-24004-4-42-2-2-22220000004i4i−4i−4i0000-22-22000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ834-4-44400-4-24004-4-42-2-2-2222000000−4i−4i4i4i0000-22-220000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ844-4-44400-4-2-400-4442-2-2-2222000000000000002-22-20000000000002323−23−23−23−232323000000000000000000000000000000
χ854-4-44400-4-2-400-4442-2-2-2222000000000000002-22-2000000000000−23−2323232323−23−23000000000000000000000000000000
χ864-4-44-40044400-44-4-4-4-4444-4000000000000004-4-4400000000000000000000000000000000000000000000000000
χ874-4-44-4004-2400-44-4222-2-2-2200000000000000-222-20000−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000
χ884-4-44-4004-2400-44-4222-2-2-2200000000000000-222-200002i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000
χ894-4-44-4004-2-4004-44222-2-2-220044-4-4000000002-2-220000-2-222-2-22200000000000000000000000000000000000000
χ904-4-44-4004-2-4004-44222-2-2-2200-4-444000000002-2-22000022-2-222-2-200000000000000000000000000000000000000

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