Finite Group Databasebeta

← Group #10776641

Character table — Group #10776641

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222222244444444488888888888888888888161616161616161616162424242424242424242424244848
order122234444666121212122444412121212244468888121212242424242424242424666121212121222224444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ61111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-111-111-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-111-111-1-1-111-1-111-1-1111111-1-1
χ911111-1-1-1-1111-1-1-1-1-1-1111-1-11111-1-1-111-1-11-111111-1-1-1-11-11111-1-1-1-11-11-11-11-111-1-11-1
χ1011111-1-1-1-1111-1-1-1-1-1-1111-1-11111-1-1-111-1-11-111111-1-1-1-11-11111-1-1-1-1-11-11-11-11-1-111-11
χ1111111-1-1-1-1111-1-1-1-1-1-1111-1-11111-1-1-1-1-1111-11-1-1-1-11111-111-1-11-1-1111-11-11-11-1-1-111-11
χ1211111-1-1-1-1111-1-1-1-1-1-1111-1-11111-1-1-1-1-1111-11-1-1-1-11111-111-1-11-1-111-11-11-11-1111-1-11-1
χ1311111-1-1-1-1111-1-1-1-1-1-1111-1-111-1-111-111-1-11-111111-1-1-1-1-11-1-1-1-111111-1-111-1-1111-1-1-11
χ1411111-1-1-1-1111-1-1-1-1-1-1111-1-111-1-111-111-1-11-111111-1-1-1-1-11-1-1-1-11111-111-1-111-1-1-1111-1
χ1511111-1-1-1-1111-1-1-1-1-1-1111-1-111-1-111-1-1-1111-11-1-1-1-111111-1-111-111-1-11-1-111-1-11-1-1111-1
χ1611111-1-1-1-1111-1-1-1-1-1-1111-1-111-1-111-1-1-1111-11-1-1-1-111111-1-111-111-1-1-111-1-111-111-1-1-11
χ172222222222222222-2-22-2-222222-2-22-20000-2-2-20000000000200-2-220000000000000000
χ182222222222222222-2-22-2-22222-222-2-20000-2-2-20000000000-20022-20000000000000000
χ192222222-2-2222-2-2-2-22-2-22-222-2-20000200002-2-20000000000000000002-200-2200000000
χ202222222-2-2222-2-2-2-22-2-22-222-2-20000200002-2-2000000000000000000-22002-200000000
χ212222222-2-2222-2-2-2-2-22-2-2222-2-20000-20000-222000000000000000000002-200-22000000
χ222222222-2-2222-2-2-2-2-22-2-2222-2-20000-20000-22200000000000000000000-22002-2000000
χ2322222-2-22222222222-2-2-22-2-2-2-2000020000-2-22000000000000000000002200-2-2000000
χ2422222-2-22222222222-2-2-22-2-2-2-2000020000-2-2200000000000000000000-2-20022000000
χ2522222-2-2222222222-22-22-2-2-2-2-20000-2000022-20000000000000000002200-2-200000000
χ2622222-2-2222222222-22-22-2-2-2-2-20000-2000022-2000000000000000000-2-2002200000000
χ2722222-2-2-2-2222-2-2-2-2222-2-2-2-2222-22-220000-22-20000000000200-22-20000000000000000
χ2822222-2-2-2-2222-2-2-2-2222-2-2-2-222-22-2220000-22-20000000000-2002-220000000000000000
χ292222-12222-1-1-1-1-1-1-122222-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ302222-12222-1-1-1-1-1-1-122222-1-1-1-12222-1-2-2-2-2-1-1-111111111-2-2-111-1-1-11100000000000000
χ312222-12222-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-2-21111111100000000000000
χ322222-12222-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-1-2-2-2-2-1-1-111111111221-1-1111-1-100000000000000
χ332222-12222-1-1-1-1-1-1-1-2-22-2-2-1-1-1-12-2-2210000111−i3−i3i3i3−i3−i3i3i300-1−i3i311-1−i3i300000000000000
χ342222-12222-1-1-1-1-1-1-1-2-22-2-2-1-1-1-12-2-2210000111i3i3−i3−i3i3i3−i3−i300-1i3−i311-1i3−i300000000000000
χ352222-12222-1-1-1-1-1-1-1-2-22-2-2-1-1-1-1-222-210000111−i3−i3i3i3−i3−i3i3i3001i3−i3-1-11i3−i300000000000000
χ362222-12222-1-1-1-1-1-1-1-2-22-2-2-1-1-1-1-222-210000111i3i3−i3−i3i3i3−i3−i3001−i3i3-1-11−i3i300000000000000
χ372222-1-2-2-2-2-1-1-11111222-2-211-1-12-22-2-100001-11−i3−i3i3i3i3i3−i3−i300-1−i3i31-11i3−i300000000000000
χ382222-1-2-2-2-2-1-1-11111222-2-211-1-12-22-2-100001-11i3i3−i3−i3−i3−i3i3i300-1i3−i31-11−i3i300000000000000
χ392222-1-2-2-2-2-1-1-11111222-2-211-1-1-22-22-100001-11−i3−i3i3i3i3i3−i3−i3001i3−i3-11-1−i3i300000000000000
χ402222-1-2-2-2-2-1-1-11111222-2-211-1-1-22-22-100001-11i3i3−i3−i3−i3−i3i3i3001−i3i3-11-1i3−i300000000000000
χ412222-1-2-2-2-2-1-1-11111-2-222211-1-122-2-2122-2-2-11-1-1-1-1-111112-2-1-1-1-1111100000000000000
χ422222-1-2-2-2-2-1-1-11111-2-222211-1-122-2-21-2-222-11-11111-1-1-1-1-22-111-111-1-100000000000000
χ432222-1-2-2-2-2-1-1-11111-2-222211-1-1-2-222122-2-2-11-1-1-1-1-11111-221111-1-1-1-100000000000000
χ442222-1-2-2-2-2-1-1-11111-2-222211-1-1-2-2221-2-222-11-11111-1-1-1-12-21-1-11-1-11100000000000000
χ454444-244-4-4-2-2-222224-4-44-4-2-2220000-20000-22200000000000000000000000000000000
χ464444-244-4-4-2-2-22222-44-4-44-2-2220000200002-2-200000000000000000000000000000000
χ474444-2-4-444-2-2-2-2-2-2-24-4-4-4422220000-2000022-200000000000000000000000000000000
χ484444-2-4-444-2-2-2-2-2-2-2-44-44-42222000020000-2-2200000000000000000000000000000000
χ4944-4-444i−4i004-4-40000000004i−4i00000002-22i−2i0002-22-22i−2i2i−2i000000000000000000000000
χ5044-4-444i−4i004-4-40000000004i−4i0000000-22−2i2i000-22-22−2i2i−2i2i000000000000000000000000
χ5144-4-44−4i4i004-4-4000000000−4i4i00000002-2−2i2i0002-22-2−2i2i−2i2i000000000000000000000000
χ5244-4-44−4i4i004-4-4000000000−4i4i0000000-222i−2i000-22-222i−2i2i−2i000000000000000000000000
χ5344-4-4-24i−4i00-2222323−23−2300000−2i2i−2i32i3000002-22i−2i000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ5444-4-4-24i−4i00-2222323−23−2300000−2i2i−2i32i300000-22−2i2i0001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ5544-4-4-24i−4i00-222−23−23232300000−2i2i2i3−2i3000002-22i−2i000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ5644-4-4-24i−4i00-222−23−23232300000−2i2i2i3−2i300000-22−2i2i0001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ5744-4-4-2−4i4i00-2222323−23−23000002i−2i2i3−2i3000002-2−2i2i000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ5844-4-4-2−4i4i00-2222323−23−23000002i−2i2i3−2i300000-222i−2i0001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ5944-4-4-2−4i4i00-222−23−232323000002i−2i−2i32i3000002-2−2i2i000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ6044-4-4-2−4i4i00-222−23−232323000002i−2i−2i32i300000-222i−2i0001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ614-4-444004-4-4-444-44-4000000000000000000000000000000000000000000000002-22-200
χ624-4-444004-4-4-444-44-400000000000000000000000000000000000000000000000-22-2200
χ634-4-44400-44-4-44-44-44000000000000000000000000000000000000000000000002-2-2200
χ644-4-44400-44-4-44-44-4400000000000000000000000000000000000000000000000-222-200
χ658-88-880000-88-8000000000000000000000000000000000000000000000000000000000
χ668-88-8-400004-4443−43−434300000000000000000000000000000000000000000000000000000
χ678-88-8-400004-44−434343−4300000000000000000000000000000000000000000000000000000
χ688-8-88-4008-844-4-44-4400000000000000000000000000000000000000000000000000000
χ698-8-88-400-8844-44-44-400000000000000000000000000000000000000000000000000000

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