Finite Group Databasebeta

← Group #10691545

Character table — Group #10691545

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order122222344444466666664444444121212121212121244888812121212121212121212242424242424242488884412121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-11-1-1111111111-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111-1-11-1-1111111111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ9111111111-1-1-1-11111111111-1-1-1-1111-1-1-1-111-111-1-11111-1-1-1-1-1-11111-1-1-1-1ii−i−i1-111-1-1i−iii−i−iii−i−ii−i
χ10111111111-1-1-1-11111111111-1-1-1-1111-1-1-1-111-111-1-11111-1-1-1-1-1-11111-1-1-1-1−i−iii1-111-1-1−ii−i−iii−i−iii−ii
χ11111111111-1-1-1-11111111111-1-1-1-1111-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-11111ii−i−i-11-1-111i−iii−i−i−i−iii−ii
χ12111111111-1-1-1-11111111111-1-1-1-1111-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-11111−i−iii-11-1-111−ii−i−iiiii−i−ii−i
χ13111111111-1-1-1-111111111-1-1-111-1111-1-1-1-11-1111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i-11-1-111i−i−i−iiiii−i−i−ii
χ14111111111-1-1-1-111111111-1-1-111-1111-1-1-1-11-1111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii-11-1-111−iiii−i−i−i−iiii−i
χ15111111111-1-1-1-111111111-1-1-111-1111-1-1-1-11-11-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−i1-111-1-1i−i−i−iii−i−iiii−i
χ16111111111-1-1-1-111111111-1-1-111-1111-1-1-1-11-11-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii1-111-1-1−iiii−i−iii−i−i−ii
χ172222222-2-222222222222-200-200-2-2-2-22222-20000000000-2-20000000000002222000000-2-20000000000
χ182222222-2-222222222222-200-200-2-2-2-22222-20000000000-2-2000000000000-2-2-2-2000000220000000000
χ192222222-2-2-2-2-2-22222222-2002002-2-2-2-2-2-2-2-20000000000220000000000002i2i−2i−2i000000−2i2i0000000000
χ202222222-2-2-2-2-2-22222222-2002002-2-2-2-2-2-2-2-2000000000022000000000000−2i−2i2i2i0000002i−2i0000000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-12-2-22-2-22-1-1-1-1-1-1-1-1-2-222221111-1-11111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-12-2-22-2-22-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1111111111111000022-1-1-1-1000000000000
χ25222222-122-2-2-2-2-1-1-1-1-1-1-1222-2-2-2-2-1-1-11111-12-222-2-2-1-1-1-1111111-1-1-1-1111100002-2-1-111000000000000
χ26222222-122-2-2-2-2-1-1-1-1-1-1-1222-2-2-2-2-1-1-11111-12-2-2-222-1-1-1-11111111111-1-1-1-10000-2211-1-1000000000000
χ27222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-222-2-1-1-11111-1-2222-2-2111111-1-1-1-1-1-1-1-111110000-2211-1-1000000000000
χ28222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-222-2-1-1-11111-1-22-2-222111111-1-1-1-11111-1-1-1-100002-2-1-111000000000000
χ292222-2-222222-2-2-2-2-2-2222-222-2-2-222-2-222-2-22-22000022-2-22-222-2-2000000000000000000000000000000
χ302222-2-222222-2-2-2-2-2-2222-2-2-2-22222-2-222-2-222-20000-2-2222-2-2-222000000000000000000000000000000
χ312222-2-2222-2-222-2-2-2-2222-222222-22-2-2-2-2222-2-2000022-2-2-22-2-222000000000000000000000000000000
χ322222-2-2222-2-222-2-2-2-2222-2-2-22-2-2-22-2-2-2-2222220000-2-222-2222-2-2000000000000000000000000000000
χ332222-2-22-2-222-2-2-2-2-2-2222200200-2-22222-2-2-20000000000-220000000000000000000000002i−2i2i−2i000000
χ342222-2-22-2-222-2-2-2-2-2-2222200200-2-22222-2-2-20000000000-22000000000000000000000000−2i2i−2i2i000000
χ352222-2-22-2-2-2-222-2-2-2-2222200-2002-222-2-222-200000000002-20000000000000000000000002-2-22000000
χ362222-2-22-2-2-2-222-2-2-2-2222200-2002-222-2-222-200000000002-2000000000000000000000000-222-2000000
χ372222-2-2-12222-2-21111-1-1-1-222-2-2-22-111-1-111-1-220000-1-111-11-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-12222-2-21111-1-1-1-222-2-2-22-111-1-111-1-220000-1-111-11-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-12222-2-21111-1-1-1-2-2-2-2222-111-1-111-12-2000011-1-1-1111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-12222-2-21111-1-1-1-2-2-2-2222-111-1-111-12-2000011-1-1-1111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-122-2-2221111-1-1-1-222222-2-11111-1-1-1-2-20000-1-1111-111-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ422222-2-2-122-2-2221111-1-1-1-222222-2-11111-1-1-1-2-20000-1-1111-111-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ432222-2-2-122-2-2221111-1-1-1-2-2-22-2-2-2-11111-1-1-122000011-1-11-1-1-111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ442222-2-2-122-2-2221111-1-1-1-2-2-22-2-2-2-11111-1-1-122000011-1-11-1-1-111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ452-2-222-22002i−2i2i−2i22-2-2-2-2200000000002i−2i2i−2i0002−2−i2i200000000002−22−2−i2i2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000001+i−1−i1−i−1+i00
χ462-2-222-22002i−2i2i−2i22-2-2-2-2200000000002i−2i2i−2i0002−2−i2i200000000002−22−2−i2i2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−1−i1+i−1+i1−i00
χ472-2-222-22002i−2i2i−2i22-2-2-2-2200000000002i−2i2i−2i000−22i2−i20000000000−22−22i2−i2i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−1−i1+i−1+i1−i00
χ482-2-222-22002i−2i2i−2i22-2-2-2-2200000000002i−2i2i−2i000−22i2−i20000000000−22−22i2−i2i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000001+i−1−i1−i−1+i00
χ492-2-222-2200−2i2i−2i2i22-2-2-2-220000000000−2i2i−2i2i0002−2i2−i200000000002−22−2i2−i2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000001−i−1+i1+i−1−i00
χ502-2-222-2200−2i2i−2i2i22-2-2-2-220000000000−2i2i−2i2i0002−2i2−i200000000002−22−2i2−i2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−1+i1−i−1−i1+i00
χ512-2-222-2200−2i2i−2i2i22-2-2-2-220000000000−2i2i−2i2i000−22−i2i20000000000−22−22−i2i2−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−1+i1−i−1−i1+i00
χ522-2-222-2200−2i2i−2i2i22-2-2-2-220000000000−2i2i−2i2i000−22−i2i20000000000−22−22−i2i2−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000001−i−1+i1+i−1−i00
χ53444444-2-4-44444-2-2-2-2-2-2-2-400-400-4222-2-2-2-220000000000220000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2-4004004222222220000000000-2-20000000000000000000000000000000000
χ554444-4-4-2-4-444-4-42222-2-2-2400400-42-2-2-2-222200000000002-20000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4442222-2-2-2400-40042-2-222-2-220000000000-220000000000000000000000000000000000
χ5744-4-40044-4000000004-4-404-400004000000-40000004-400000000000000000000000000000000000000
χ5844-4-40044-4000000004-4-40-4400004000000-4000000-4400000000000000000000000000000000000000
χ5944-4-4004-44000000004-4-400004i−4i0-40000004000000000000004i−4i000000000000000000000000000000
χ6044-4-4004-44000000004-4-40000−4i4i0-4000000400000000000000−4i4i000000000000000000000000000000
χ6144-4-400-24-40000−2i32i3−2i32i3-22204-40000-2−2i32i300002000000-22−2i32i3000000000000000000000000000000000000
χ6244-4-400-24-40000−2i32i3−2i32i3-2220-440000-2−2i32i3000020000002-22i3−2i3000000000000000000000000000000000000
χ6344-4-400-24-400002i3−2i32i3−2i3-22204-40000-22i3−2i300002000000-222i3−2i3000000000000000000000000000000000000
χ6444-4-400-24-400002i3−2i32i3−2i3-2220-440000-22i3−2i3000020000002-2−2i32i3000000000000000000000000000000000000
χ6544-4-400-2-440000−2i32i3−2i32i3-22200004i−4i022i3−2i30000-200000000000023−23−2i2i000000000000000000000000000000
χ6644-4-400-2-440000−2i32i3−2i32i3-2220000−4i4i022i3−2i30000-2000000000000−23232i−2i000000000000000000000000000000
χ6744-4-400-2-4400002i3−2i32i3−2i3-22200004i−4i02−2i32i30000-2000000000000−2323−2i2i000000000000000000000000000000
χ6844-4-400-2-4400002i3−2i32i3−2i3-2220000−4i4i02−2i32i30000-200000000000023−232i−2i000000000000000000000000000000
χ694-4-444-4-2004i−4i4i−4i-2-22222-20000000000−2i2i−2i2i00022−22−2i22i20000000000−22−22i2−i2i2−i20000000000000000000000
χ704-4-444-4-2004i−4i4i−4i-2-22222-20000000000−2i2i−2i2i000−22222i2−2i200000000002−22−2−i2i2−i2i20000000000000000000000
χ714-4-444-4-200−4i4i−4i4i-2-22222-200000000002i−2i2i−2i00022−222i2−2i20000000000−22−22−i2i2−i2i20000000000000000000000
χ724-4-444-4-200−4i4i−4i4i-2-22222-200000000002i−2i2i−2i000−2222−2i22i200000000002−22−2i2−i2i2−i20000000000000000000000
χ734-4-44-444004i−4i−4i4i-4-444-4-4400000000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ744-4-44-44400−4i4i4i−4i-4-444-4-440000000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ754-4-44-44-2004i−4i−4i4i22-2-222-20000000000−2i2i2i−2i00000000000000000i6−i6−i6i66−6−660000000000000000000000
χ764-4-44-44-2004i−4i−4i4i22-2-222-20000000000−2i2i2i−2i00000000000000000−i6i6i6−i6−666−60000000000000000000000
χ774-4-44-44-200−4i4i4i−4i22-2-222-200000000002i−2i−2i2i00000000000000000i6−i6−i6i6−666−60000000000000000000000
χ784-4-44-44-200−4i4i4i−4i22-2-222-200000000002i−2i−2i2i00000000000000000−i6i6i6−i66−6−660000000000000000000000
χ798-88-80080000000000-88-80000000000000000000000000000000000000000000000000000000000000
χ808-88-800-4000000−4i34i34i3−4i34-440000000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000004i3−4i3−4i34i34-440000000000000000000000000000000000000000000000000000000000000

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