Finite Group Databasebeta

← Group #10696575

Character table — Group #10696575

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order122222344666444446612121212121212128888121224242424242424242444661212121212124444448888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-1-1-111
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111
χ92222222222222-2-2-2-222-2-2-2-222-2-20000-220000000000000000000000002-20000
χ102222222222222-2-2-2-222-2-2-2-222-2-20000-22000000000000000000000000-220000
χ112222222-2-2222-22-2-222222-2-2-2-2-2-200002-20000000000000000000022-2-2000000
χ122222222-2-2222-22-2-222222-2-2-2-2-2-200002-200000000000000000000-2-222000000
χ132222222-2-2222-2-222-222-2-222-2-2220000-2-20000000002-20000022-2-20000000000
χ142222222-2-2222-2-222-222-2-222-2-2220000-2-2000000000-2200000-2-2220000000000
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111112-2-22-1-1-1-111110000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-222-21111-1-1-1-10000000000
χ19222222-1-2-2-1-1-1-2-222-2-1-111-1-111-1-1000011−i3−i3−i3−i3i3i3i3i302-20−i3i3−i3i3-1-1110000000000
χ20222222-1-2-2-1-1-1-2-222-2-1-111-1-111-1-1000011−i3−i3−i3−i3i3i3i3i30-220i3−i3i3−i311-1-10000000000
χ21222222-1-2-2-1-1-1-2-222-2-1-111-1-111-1-1000011i3i3i3i3−i3−i3−i3−i302-20i3−i3i3−i3-1-1110000000000
χ22222222-1-2-2-1-1-1-2-222-2-1-111-1-111-1-1000011i3i3i3i3−i3−i3−i3−i30-220−i3i3−i3i311-1-10000000000
χ232222-2-2222222-22-22-2-2-222-2-222220000-2-200000000200-222-2-200000000000000
χ242222-2-2222222-22-22-2-2-222-2-222220000-2-200000000-2002-2-22200000000000000
χ252222-2-2222222-2-22-22-2-2-2-22222-2-200002-2000000000000000000000000002-200
χ262222-2-2222222-2-22-22-2-2-2-22222-2-200002-200000000000000000000000000-2200
χ272222-2-22-2-2222222-2-2-2-22222-2-2-2-20000-2200000000000000000000000000002i−2i
χ282222-2-22-2-2222222-2-2-2-22222-2-2-2-20000-220000000000000000000000000000−2i2i
χ292222-2-22-2-22222-2-222-2-2-2-2-2-2-2-22222-2-22222-2-222-2-20000000000000000000000
χ302222-2-22-2-22222-2-222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2220000000000000000000000
χ312222-2-2-122-1-1-1-22-22-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i3200-2-1-111−i3i3−i3i30000000000
χ322222-2-2-122-1-1-1-22-22-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i3-200211-1-1i3−i3i3−i30000000000
χ332222-2-2-122-1-1-1-22-22-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i3200-2-1-111i3−i3i3−i30000000000
χ342222-2-2-122-1-1-1-22-22-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i3-200211-1-1−i3i3−i3i30000000000
χ352222-2-2-1-2-2-1-1-12-2-22211111111-1-122-2-2-1-1-1-111-1-1110000−i3i3i3−i3−i3i3i3−i30000000000
χ362222-2-2-1-2-2-1-1-12-2-22211111111-1-122-2-2-1-1-1-111-1-1110000i3−i3−i3i3i3−i3−i3i30000000000
χ372222-2-2-1-2-2-1-1-12-2-22211111111-1-1-2-222-1-111-1-111-1-10000−i3i3i3−i3i3−i3−i3i30000000000
χ382222-2-2-1-2-2-1-1-12-2-22211111111-1-1-2-222-1-111-1-111-1-10000i3−i3−i3i3−i3i3i3−i30000000000
χ39444444-244-2-2-24-4-4-4-4-2-22222-2-22200002-2000000000000000000000000000000
χ40444444-2-4-4-2-2-2-44-4-44-2-2-2-22222220000-22000000000000000000000000000000
χ414444-4-4-244-2-2-2-4-44-442222-2-2-2-2220000-22000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-2444-4-422-2-2-2-2222200002-2000000000000000000000000000000
χ4344-4-40044-4-4-44000000000004-400000000000000000000000000002i−2i2i−2i000000
χ4444-4-40044-4-4-44000000000004-40000000000000000000000000000−2i2i−2i2i000000
χ4544-4-4004-44-4-4400000000000-4400000000000000000000000000002i−2i−2i2i000000
χ4644-4-4004-44-4-4400000000000-440000000000000000000000000000−2i2i2i−2i000000
χ474-4-444-4400-44-4000004-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ484-4-444-4400-44-4000004-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ494-4-444-4-2002-2200000-2200−2i32i300−2i32i32i−2i2i−2i002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ110000000000000000000000
χ504-4-444-4-2002-2200000-2200−2i32i300−2i32i3−2i2i−2i2i00−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ110000000000000000000000
χ514-4-444-4-2002-2200000-22002i3−2i3002i3−2i32i−2i2i−2i002ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ70000000000000000000000
χ524-4-444-4-2002-2200000-22002i3−2i3002i3−2i3−2i2i−2i2i00−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ70000000000000000000000
χ534-4-44-44400-44-400000-44000000002i−2i−2i2i002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ544-4-44-44400-44-400000-4400000000−2i2i2i−2i00−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ554-4-44-44-2002-22000002-200−2i32i3002i3−2i32i−2i−2i2i002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ70000000000000000000000
χ564-4-44-44-2002-22000002-200−2i32i3002i3−2i3−2i2i2i−2i00−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ70000000000000000000000
χ574-4-44-44-2002-22000002-2002i3−2i300−2i32i32i−2i−2i2i002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ110000000000000000000000
χ584-4-44-44-2002-22000002-2002i3−2i300−2i32i3−2i2i2i−2i00−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ110000000000000000000000
χ5988-8-800-48-844-400000000000-4400000000000000000000000000000000000000
χ6088-8-800-4-8844-4000000000004-400000000000000000000000000000000000000
χ618-88-8008008-8-8000000000000000000000000000000000000000000000000000
χ628-88-800-400-4440000000−4i34i3000000000000000000000000000000000000000000
χ638-88-800-400-44400000004i3−4i3000000000000000000000000000000000000000000

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