Finite Group Databasebeta

← Group #10858711

Character table — Group #10858711

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222444444448888888888888888888888121212121212121216161616161616161624242424242424244848
order122222344446666666888812121212444444448812121212242424242424242422444444412121212121212124444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-11
χ411111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1111-1-11-1
χ511111111111111111111-1-111111111-1-1-1-11-1-1-1-1-11111-1-1-1-111111111-11111-1-1-1-11-11-111-1-1-1-1
χ611111111111111111111-1-111111111-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-11111
χ711111111111111111111-1-11111-1-1-1-111-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-11-1
χ811111111111111111111-1-11111-1-1-1-111-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11111-11
χ9111111111111111111-1-111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111-1
χ10111111111111111111-1-111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-111-1-11111-1-1-1-1-11
χ11111111111111111111-1-1111111-1-11111-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-111-1-111-11-11-1-111-1-1
χ12111111111111111111-1-1111111-1-11111-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1111-11-111-1-111
χ13111111111111111111-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-111-11-1111-1-1-11
χ14111111111111111111-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1111-11-1-1-1111-1
χ15111111111111111111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ16111111111111111111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111111111-1-1
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-1-1-1-1-10000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-100000000-2111111110000000000
χ19222222-12222-1-1-1-1-1-1-122-2-2-1-1-1-12222-2-2-2-22-21111-1-1-1-1111100000000-2-1-1-1-111110000000000
χ20222222-12222-1-1-1-1-1-1-122-2-2-1-1-1-1-2-2-2-222-2-22-21111-1-1-1-111110000000021111-1-1-1-10000000000
χ21222222-12222-1-1-1-1-1-1-1-2-222-1-1-1-122-2-2-2-2-2-2-2211111111-1-1-1-1000000002-1-111-1-1110000000000
χ22222222-12222-1-1-1-1-1-1-1-2-222-1-1-1-1-2-22222-2-2-2211111111-1-1-1-100000000-211-1-111-1-10000000000
χ23222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-22222-2-2-1-1-1-11111111100000000-2-1-11111-1-10000000000
χ24222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-222-2-222-2-2-1-1-1-11111111100000000211-1-1-1-1110000000000
χ252222-2-222-2-222-2-2-2-22200222-22-2000000000-20000000022-2-2000022-2-2000000000020-2000000
χ262222-2-222-2-222-2-2-2-22200222-22-2000000000-20000000022-2-20000-2-2220000000000-202000000
χ272222-2-222-2-222-2-2-2-22200-2-22-22-2000000000200000000-2-222000022-2-20000000000-202000000
χ282222-2-222-2-222-2-2-2-22200-2-22-22-2000000000200000000-2-2220000-2-222000000000020-2000000
χ292222-2-22-222-22-2-2-2-2222200-22-2200000000-20000022-2-2000022-2-2000000000000020-20000000
χ302222-2-22-222-22-2-2-2-2222200-22-2200000000-20000022-2-20000-2-2220000000000000-2020000000
χ312222-2-22-222-22-2-2-2-222-2-200-22-2200000000200000-2-222000022-2-20000000000000-2020000000
χ322222-2-22-222-22-2-2-2-222-2-200-22-2200000000200000-2-2220000-2-222000000000000020-20000000
χ3322-2-22-2222-2-2-222-2-22-2000022-2-22-2000000000000000000002-22-2000002-200000000002-20000
χ3422-2-22-2222-2-2-222-2-22-2000022-2-22-200000000000000000000-22-22000002-20000000000-220000
χ3522-2-22-2222-2-2-222-2-22-2000022-2-2-22000000000000000000002-22-200000-220000000000-220000
χ3622-2-22-2222-2-2-222-2-22-2000022-2-2-2200000000000000000000-22-2200000-2200000000002-20000
χ3722-2-22-22-2-222-222-2-22-20000-2-22200002i−2i000000000000000000002i−2i2i−2i00000002i−2i0000002-200
χ3822-2-22-22-2-222-222-2-22-20000-2-22200002i−2i00000000000000000000−2i2i−2i2i00000002i−2i000000-2200
χ3922-2-22-22-2-222-222-2-22-20000-2-2220000−2i2i000000000000000000002i−2i2i−2i0000000−2i2i000000-2200
χ4022-2-22-22-2-222-222-2-22-20000-2-2220000−2i2i00000000000000000000−2i2i−2i2i0000000−2i2i0000002-200
χ4122-2-2-222-22-22-2-2-2222-20000-222-2002i−2i0000000000000000002-2-222i−2i−2i2i0002i−2i00000000000000
χ4222-2-2-222-22-22-2-2-2222-20000-222-2002i−2i000000000000000000-222-2−2i2i2i−2i0002i−2i00000000000000
χ4322-2-2-222-22-22-2-2-2222-20000-222-200−2i2i0000000000000000002-2-22−2i2i2i−2i000−2i2i00000000000000
χ4422-2-2-222-22-22-2-2-2222-20000-222-200−2i2i000000000000000000-222-22i−2i−2i2i000−2i2i00000000000000
χ454444444-4-4-4-444444440000-4-4-4-40000000000000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000000000−2i3−2i32i32i300000000000000000000000000000000000
χ47444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000002i32i3−2i3−2i300000000000000000000000000000000000
χ484444-4-4-24-4-44-22222-2-20044-22-22000000000-400000000-2-222000000000000000000000000000
χ494444-4-4-24-4-44-22222-2-200-4-4-22-2200000000040000000022-2-2000000000000000000000000000
χ504444-4-4-2-444-4-22222-2-244002-22-200000000-400000-2-2220000000000000000000000000000000
χ514444-4-4-2-444-4-22222-2-2-4-4002-22-20000000040000022-2-20000000000000000000000000000000
χ5244-4-44-4-244-4-42-2-222-220000-2-2224-400000000000000000000000000000-220000000000000000
χ5344-4-44-4-244-4-42-2-222-220000-2-222-44000000000000000000000000000002-20000000000000000
χ5444-4-44-4-2-4-4442-2-222-22000022-2-200004i−4i0000000000000000000000000000000−2i2i0000000000
χ5544-4-44-4-2-4-4442-2-222-22000022-2-20000−4i4i00000000000000000000000000000002i−2i0000000000
χ5644-4-4-4444-44-4-4-4-4444-400004-4-440000000000000000000000000000000000000000000000000
χ5744-4-4-44-24-44-4222-2-2-220000-222-20000000000000000000000000000000000023−23000000000000
χ5844-4-4-44-24-44-4222-2-2-220000-222-200000000000000000000000000000000000−2323000000000000
χ5944-4-4-44-2-44-44222-2-2-2200002-2-22004i−4i00000000000000000000000000000−2i2i00000000000000
χ6044-4-4-44-2-44-44222-2-2-2200002-2-2200−4i4i000000000000000000000000000002i−2i00000000000000
χ614-44-4004000040000-4-422−2222−2200000000002-2002-22-222−220022−2200000000000000000000000000000
χ624-44-4004000040000-4-422−22−22220000000000-2200-22-2222−2200−222200000000000000000000000000000
χ634-44-4004000040000-4-4−222222−220000000000-2200-22-22−22220022−2200000000000000000000000000000
χ644-44-4004000040000-4-4−2222−222200000000002-2002-22-2−222200−222200000000000000000000000000000
χ654-44-400-20000-2−2i32i3−2i32i32222−2222−2200000000002-200−1−i31+i3−1+i31−i3−22i6−i6−22i6−i6000000000000000000000000000
χ664-44-400-20000-2−2i32i3−2i32i32222−22−22220000000000-22001+i3−1−i31−i3−1+i3−22i6−i62−2−i6i6000000000000000000000000000
χ674-44-400-20000-2−2i32i3−2i32i322−222222−220000000000-22001+i3−1−i31−i3−1+i32−2−i6i6−22i6−i6000000000000000000000000000
χ684-44-400-20000-2−2i32i3−2i32i322−2222−222200000000002-200−1−i31+i3−1+i31−i32−2−i6i62−2−i6i6000000000000000000000000000
χ694-44-400-20000-22i3−2i32i3−2i32222−2222−2200000000002-200−1+i31−i3−1−i31+i3−22−i6i6−22−i6i6000000000000000000000000000
χ704-44-400-20000-22i3−2i32i3−2i32222−22−22220000000000-22001−i3−1+i31+i3−1−i3−22−i6i62−2i6−i6000000000000000000000000000
χ714-44-400-20000-22i3−2i32i3−2i322−222222−220000000000-22001−i3−1+i31+i3−1−i32−2i6−i6−22−i6i6000000000000000000000000000
χ724-44-400-20000-22i3−2i32i3−2i322−2222−222200000000002-200−1+i31−i3−1−i31+i32−2i6−i62−2i6−i6000000000000000000000000000
χ738-8-880080000-80000-88000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400004−4i34i34i3−4i34-4000000000000000000000000000000000000000000000000000000000
χ758-8-8800-4000044i3−4i3−4i34i34-4000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).