Finite Group Databasebeta

← Group #10696596

Character table — Group #10696596

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order12222234466644444661212121212121212888812122424242424242424444412121212121212124444248888
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
χ9222222222222-2-22-2-22222-2-2-2-2-2-200002-20000000000000000000000002-20000
χ10222222222222-2-22-2-22222-2-2-2-2-2-200002-2000000000000000000000000-220000
χ112222222-2-22222-2-2-2222-2-222-2-2-2-20000-220000000000000000000022-2-2000000
χ122222222-2-22222-2-2-2222-2-222-2-2-2-20000-2200000000000000000000-2-222000000
χ132222222-2-2222-22-22-222-2-2-2-222220000-2-20000000002-20000022-2-20000000000
χ142222222-2-2222-22-22-222-2-2-2-222220000-2-2000000000-2200000-2-2220000000000
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
χ19222222-1-2-2-1-1-1-22-22-2-1-11111-1-1-1-1000011−i3−i3−i3−i3i3i3i3i302-20−i3−i3i3i3-1-1110000000000
χ20222222-1-2-2-1-1-1-22-22-2-1-11111-1-1-1-1000011−i3−i3−i3−i3i3i3i3i30-220i3i3−i3−i311-1-10000000000
χ21222222-1-2-2-1-1-1-22-22-2-1-11111-1-1-1-1000011i3i3i3i3−i3−i3−i3−i302-20i3i3−i3−i3-1-1110000000000
χ22222222-1-2-2-1-1-1-22-22-2-1-11111-1-1-1-1000011i3i3i3i3−i3−i3−i3−i30-220−i3−i3i3i311-1-10000000000
χ232222-2-22222222-2-22-2-2-22222-2-2220000-2-200000000200-22-22-200000000000000
χ242222-2-22222222-2-22-2-2-22222-2-2220000-2-200000000-2002-22-2200000000000000
χ252222-2-2222222-22-2-22-2-222-2-222-2-20000-22000000000000000000000000002-200
χ262222-2-2222222-22-2-22-2-222-2-222-2-20000-2200000000000000000000000000-2200
χ272222-2-22-2-2222222-2-2-2-2-2-22222-2-200002-200000000000000000000000000002i−2i
χ282222-2-22-2-2222222-2-2-2-2-2-22222-2-200002-20000000000000000000000000000−2i2i
χ292222-2-22-2-2222-2-2222-2-2-2-2-2-2-2-22222-2-22222-2-222-2-20000000000000000000000
χ302222-2-22-2-2222-2-2222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2220000000000000000000000
χ312222-2-2-122-1-1-12-2-22-211-1-1-1-111-1-1000011−i3−i3i3i3i3i3−i3−i3200-2-11-11−i3i3−i3i30000000000
χ322222-2-2-122-1-1-12-2-22-211-1-1-1-111-1-1000011−i3−i3i3i3i3i3−i3−i3-20021-11-1i3−i3i3−i30000000000
χ332222-2-2-122-1-1-12-2-22-211-1-1-1-111-1-1000011i3i3−i3−i3−i3−i3i3i3200-2-11-11i3−i3i3−i30000000000
χ342222-2-2-122-1-1-12-2-22-211-1-1-1-111-1-1000011i3i3−i3−i3−i3−i3i3i3-20021-11-1−i3i3−i3i30000000000
χ352222-2-2-1-2-2-1-1-1-2-222211111111-1-122-2-2-1-1-1-111-1-1110000−i3i3i3−i3−i3i3i3−i30000000000
χ362222-2-2-1-2-2-1-1-1-2-222211111111-1-122-2-2-1-1-1-111-1-1110000i3−i3−i3i3i3−i3−i3i30000000000
χ372222-2-2-1-2-2-1-1-1-2-222211111111-1-1-2-222-1-111-1-111-1-10000−i3i3i3−i3i3−i3−i3i30000000000
χ382222-2-2-1-2-2-1-1-1-2-222211111111-1-1-2-222-1-111-1-111-1-10000i3−i3−i3i3−i3i3i3−i30000000000
χ39444444-244-2-2-2-4-44-4-4-2-2-2-22222220000-22000000000000000000000000000000
χ40444444-2-4-4-2-2-24-4-4-44-2-222-2-2222200002-2000000000000000000000000000000
χ414444-4-4-244-2-2-2-44-4-4422-2-222-2-22200002-2000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-2444-4-42222-2-2-2-2220000-22000000000000000000000000000000
χ434-44-44-4400-4-44000004-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ444-44-44-4400-4-44000004-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ454-44-44-4-20022-200000-220000−2i32i3−2i32i32i−2i2i−2i002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ110000000000000000000000
χ464-44-44-4-20022-200000-220000−2i32i3−2i32i3−2i2i−2i2i00−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ110000000000000000000000
χ474-44-44-4-20022-200000-2200002i3−2i32i3−2i32i−2i2i−2i002ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ70000000000000000000000
χ484-44-44-4-20022-200000-2200002i3−2i32i3−2i3−2i2i−2i2i00−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ70000000000000000000000
χ494-44-4-44400-4-4400000-44000000002i−2i−2i2i002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ504-44-4-44400-4-4400000-4400000000−2i2i2i−2i00−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ514-44-4-44-20022-2000002-20000−2i32i32i3−2i32i−2i−2i2i002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ70000000000000000000000
χ524-44-4-44-20022-2000002-20000−2i32i32i3−2i3−2i2i2i−2i00−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ70000000000000000000000
χ534-44-4-44-20022-2000002-200002i3−2i3−2i32i32i−2i−2i2i002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ110000000000000000000000
χ544-44-4-44-20022-2000002-200002i3−2i3−2i32i3−2i2i2i−2i00−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ110000000000000000000000
χ554-4-440044-44-4-400000004-4000000000000000000000000000000002i−2i2i−2i000000
χ564-4-440044-44-4-400000004-400000000000000000000000000000000−2i2i−2i2i000000
χ574-4-44004-444-4-40000000-44000000000000000000000000000000002i−2i−2i2i000000
χ584-4-44004-444-4-40000000-4400000000000000000000000000000000−2i2i2i−2i000000
χ5988-8-800800-88-8000000000000000000000000000000000000000000000000000
χ6088-8-800-4004-44000000000−4i34i30000000000000000000000000000000000000000
χ6188-8-800-4004-440000000004i3−4i30000000000000000000000000000000000000000
χ628-8-8800-48-8-4440000000-44000000000000000000000000000000000000000000
χ638-8-8800-4-88-44400000004-4000000000000000000000000000000000000000000

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