Finite Group Databasebeta

← Group #10691663

Character table — Group #10691663

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222222344446661212121224466668888121212126888888122424242424242424242424242424242488888824242424244444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111111111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ9111111-1-11-1-1-1-1111-1-1-1-1-11111-1-1ii−i−i11-1-1-1i−i11-1-11iiii−i−i−i−i1111-1-1-1-1ii−i−ii−iii−i−i1-11-1ii−i−ii−i1-1
χ10111111-1-11-1-1-1-1111-1-1-1-1-11111-1-1ii−i−i11-1-1-1i−i11-1-11iiii−i−i−i−i1111-1-1-1-1−i−iiii−iii−i−i-11-11−i−iii−ii-11
χ11111111-1-11-1-1-1-1111-1-1-1-1-11111-1-1ii−i−i11-1-1-1i−i-1-1111iiii−i−i−i−i-1-1-1-11111ii−i−i−ii−i−iii1-11-1−i−iiii−i-11
χ12111111-1-11-1-1-1-1111-1-1-1-1-11111-1-1ii−i−i11-1-1-1i−i-1-1111iiii−i−i−i−i-1-1-1-11111−i−iii−ii−i−iii-11-11ii−i−i−ii1-1
χ13111111-1-11-1-1-1-1111-1-1-1-1-11111-1-1−i−iii11-1-1-1−ii11-1-11−i−i−i−iiiii1111-1-1-1-1ii−i−i−ii−i−iii-11-11ii−i−ii−i-11
χ14111111-1-11-1-1-1-1111-1-1-1-1-11111-1-1−i−iii11-1-1-1−ii11-1-11−i−i−i−iiiii1111-1-1-1-1−i−iii−ii−i−iii1-11-1−i−iii−ii1-1
χ15111111-1-11-1-1-1-1111-1-1-1-1-11111-1-1−i−iii11-1-1-1−ii-1-1111−i−i−i−iiiii-1-1-1-11111ii−i−ii−iii−i−i-11-11−i−iiii−i1-1
χ16111111-1-11-1-1-1-1111-1-1-1-1-11111-1-1−i−iii11-1-1-1−ii-1-1111−i−i−i−iiiii-1-1-1-11111−i−iiii−iii−i−i1-11-1ii−i−i−ii-11
χ17222222222-2-2-2-2222-2-2-2-22-2-222220000-2-2-2-22000000-200000000000000002i2i−2i−2i00000000000000−2i2i00
χ18222222222-2-2-2-2222-2-2-2-22-2-222220000-2-2-2-22000000-20000000000000000−2i−2i2i2i000000000000002i−2i00
χ1922222222-12222-1-1-1-1-1-1-1222-1-1-1-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-1222-1-1-1-12222-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ2122222222-12222-1-1-1-1-1-1-1222-1-1-1-1-2-2-2-2-1-1-1-1-1-2-22222-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ2222222222-12222-1-1-1-1-1-1-1222-1-1-1-1-2-2-2-2-1-1-1-1-1-2-2-2-2-2-2-11111111111111111000022-1-1-1-1000000000000
χ23222222-2-2222222222222-2-2-222-2-20000-2-222-2000000-20000000000000000222200000000000000-2-200
χ24222222-2-2222222222222-2-2-222-2-20000-2-222-2000000-20000000000000000-2-2-2-2000000000000002200
χ25222222-2-2-1-2-2-2-2-1-1-11111-222-1-1112i2i−2i−2i-1-11112i−2i22-2-2-1−i−i−i−iiiii-1-1-1-1111100002i−2i−i−iii000000000000
χ26222222-2-2-1-2-2-2-2-1-1-11111-222-1-1112i2i−2i−2i-1-11112i−2i-2-222-1−i−i−i−iiiii1111-1-1-1-10000−2i2iii−i−i000000000000
χ27222222-2-2-1-2-2-2-2-1-1-11111-222-1-111−2i−2i2i2i-1-1111−2i2i22-2-2-1iiii−i−i−i−i-1-1-1-111110000−2i2iii−i−i000000000000
χ28222222-2-2-1-2-2-2-2-1-1-11111-222-1-111−2i−2i2i2i-1-1111−2i2i-2-222-1iiii−i−i−i−i1111-1-1-1-100002i−2i−i−iii000000000000
χ292222-2-222222-2-22222222-2-22-2-222000022-2-2-2000000-20000000000000000000000000022-2-200000000
χ302222-2-222222-2-22222222-2-22-2-222000022-2-2-2000000-200000000000000000000000000-2-22200000000
χ312222-2-2222-2-222222-2-2-2-2-22-2-2-2222222-2-222-2-2-20000222-2-222-2-2000000000000000000000000000000
χ322222-2-2222-2-222222-2-2-2-2-22-2-2-222-2-2-2-2-2-222-22200002-2-222-2-222000000000000000000000000000000
χ332222-2-222-1-2-222-1-1-11111-22-211-1-1222211-1-11-2-20000-1-1-111-1-11133−3−333−3−30000003−33−3000000000000
χ342222-2-222-1-2-222-1-1-11111-22-211-1-1222211-1-11-2-20000-1-1-111-1-111−3−333−3−333000000−33−33000000000000
χ352222-2-222-1-2-222-1-1-11111-22-211-1-1-2-2-2-211-1-11220000-111-1-111-1-133−3−333−3−3000000−33−33000000000000
χ362222-2-222-1-2-222-1-1-11111-22-211-1-1-2-2-2-211-1-11220000-111-1-111-1-1−3−333−3−3330000003−33−3000000000000
χ372222-2-2-2-2222-2-2222222222-2-2-2-2-22i2i−2i−2i-2-2-2-22−2i2i000022i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ382222-2-2-2-2222-2-2222222222-2-2-2-2-2−2i−2i2i2i-2-2-2-222i−2i00002−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ392222-2-2-2-22-2-222222-2-2-2-22-22-2-2-2-2000022222000000-2000000000000000000000000002-2-2200000000
χ402222-2-2-2-22-2-222222-2-2-2-22-22-2-2-2-2000022222000000-200000000000000000000000000-222-200000000
χ412222-2-2-2-2-122-2-2-1-1-1-1-1-1-122-211112i2i−2i−2i1111-1−2i2i0000-1−i−iiiii−i−i33−3−3−3−333000000i3−i3−i3i3000000000000
χ422222-2-2-2-2-122-2-2-1-1-1-1-1-1-122-211112i2i−2i−2i1111-1−2i2i0000-1−i−iiiii−i−i−3−33333−3−3000000−i3i3i3−i3000000000000
χ432222-2-2-2-2-122-2-2-1-1-1-1-1-1-122-21111−2i−2i2i2i1111-12i−2i0000-1ii−i−i−i−iii33−3−3−3−333000000−i3i3i3−i3000000000000
χ442222-2-2-2-2-122-2-2-1-1-1-1-1-1-122-21111−2i−2i2i2i1111-12i−2i0000-1ii−i−i−i−iii−3−33333−3−3000000i3−i3−i3i3000000000000
χ452-22-22-20022i−2i2i−2i2-2-22i2i−2i−2i0002-2000000002i−2i0002−2−i2i20000000002−22−2−i2i2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000001+i−1−i1−i−1+i0000
χ462-22-22-20022i−2i2i−2i2-2-22i2i−2i−2i0002-2000000002i−2i0002−2−i2i20000000002−22−2−i2i2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−1−i1+i−1+i1−i0000
χ472-22-22-20022i−2i2i−2i2-2-22i2i−2i−2i0002-2000000002i−2i000−22i2−i2000000000−22−22i2−i2i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000−1−i1+i−1+i1−i0000
χ482-22-22-20022i−2i2i−2i2-2-22i2i−2i−2i0002-2000000002i−2i000−22i2−i2000000000−22−22i2−i2i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000001+i−1−i1−i−1+i0000
χ492-22-22-2002−2i2i−2i2i2-2-2−2i−2i2i2i0002-200000000−2i2i0002−2i2−i20000000002−22−2i2−i2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000001−i−1+i1+i−1−i0000
χ502-22-22-2002−2i2i−2i2i2-2-2−2i−2i2i2i0002-200000000−2i2i0002−2i2−i20000000002−22−2i2−i2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000−1+i1−i−1−i1+i0000
χ512-22-22-2002−2i2i−2i2i2-2-2−2i−2i2i2i0002-200000000−2i2i000−22−i2i2000000000−22−22−i2i2−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000−1+i1−i−1−i1+i0000
χ522-22-22-2002−2i2i−2i2i2-2-2−2i−2i2i2i0002-200000000−2i2i000−22−i2i2000000000−22−22−i2i2−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000001−i−1+i1+i−1−i0000
χ5344444444-2-4-4-4-4-2-2-222224-4-4-2-2-2-200002222-2000000200000000000000000000000000000000000000
χ54444444-4-4-24444-2-2-2-2-2-2-2-4-4-4-2-222000022-2-22000000200000000000000000000000000000000000000
χ554444-4-444-244-4-4-2-2-2-2-2-2-2-4-4422-2-20000-2-2222000000200000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-444-2-2-222224-4422220000-2-2-2-2-2000000200000000000000000000000000000000000000
χ5744-4-4004-440000-44-40000000004-422−2222−2200000000000022−220022−2200000000000000000000000000000000
χ5844-4-4004-440000-44-40000000004-4−2222−2222000000000000−222200−222200000000000000000000000000000000
χ5944-4-4004-4-200002-2223−2323−2300000-2222−2222−2223−230000000000−226−6−226−6000000000000000000000000000000
χ6044-4-4004-4-200002-2223−2323−2300000-22−2222−222223−2300000000002−2−662−2−66000000000000000000000000000000
χ6144-4-4004-4-200002-22−2323−232300000-2222−2222−22−23230000000000−22−66−22−66000000000000000000000000000000
χ6244-4-4004-4-200002-22−2323−232300000-22−2222−2222−232300000000002−26−62−26−6000000000000000000000000000000
χ6344-4-400-4440000-44-4000000000-44−2i22i22i2−2i2000000000000−2i22i2002i2−2i200000000000000000000000000000000
χ6444-4-400-4440000-44-4000000000-442i2−2i2−2i22i20000000000002i2−2i200−2i22i200000000000000000000000000000000
χ6544-4-400-44-200002-2223−2323−23000002-2−2i22i22i2−2i2−23230000000000i2−i2i6−i6−i2i2−i6i6000000000000000000000000000000
χ6644-4-400-44-200002-2223−2323−23000002-22i2−2i2−2i22i2−23230000000000−i2i2−i6i6i2−i2i6−i6000000000000000000000000000000
χ6744-4-400-44-200002-22−2323−2323000002-2−2i22i22i2−2i223−230000000000i2−i2−i6i6−i2i2i6−i6000000000000000000000000000000
χ6844-4-400-44-200002-22−2323−2323000002-22i2−2i2−2i22i223−230000000000−i2i2i6−i6i2−i2−i6i6000000000000000000000000000000
χ694-44-44-400-24i−4i4i−4i-222−2i−2i2i2i000-2200000000−2i2i00022−22−2i22i2000000000−22−22i2−i2i2−i20000000000000000000000
χ704-44-44-400-24i−4i4i−4i-222−2i−2i2i2i000-2200000000−2i2i000−22222i2−2i20000000002−22−2−i2i2−i2i20000000000000000000000
χ714-44-44-400-2−4i4i−4i4i-2222i2i−2i−2i000-22000000002i−2i00022−222i2−2i2000000000−22−22−i2i2−i2i20000000000000000000000
χ724-44-44-400-2−4i4i−4i4i-2222i2i−2i−2i000-22000000002i−2i000−2222−2i22i20000000002−22−2i2−i2i2−i20000000000000000000000
χ734-44-4-440044i−4i−4i4i4-4-44i4i−4i−4i000-4400000000−4i4i0000000000000000000000000000000000000000000000
χ744-44-4-44004−4i4i4i−4i4-4-4−4i−4i4i4i000-44000000004i−4i0000000000000000000000000000000000000000000000
χ754-44-4-4400-24i−4i−4i4i-222−2i−2i2i2i0002-2000000002i−2i00000000000000006−6−66i6−i6−i6i60000000000000000000000
χ764-44-4-4400-24i−4i−4i4i-222−2i−2i2i2i0002-2000000002i−2i0000000000000000−666−6−i6i6i6−i60000000000000000000000
χ774-44-4-4400-2−4i4i4i−4i-2222i2i−2i−2i0002-200000000−2i2i00000000000000006−6−66−i6i6i6−i60000000000000000000000
χ784-44-4-4400-2−4i4i4i−4i-2222i2i−2i−2i0002-200000000−2i2i0000000000000000−666−6i6−i6−i6i60000000000000000000000
χ798-8-88000080000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-880000-4000044-4−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000
χ818-8-880000-4000044-44i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000

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