Finite Group Databasebeta

← Group #10696517

Character table — Group #10696517

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11111111222222224444448888881616161616161616161616161616161616162424242424242424242424244848
order1222222236666666444444121212121212244444661212121212121212121288888888888844
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-11-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111111111-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1
χ922222222222222222-2-22-2-222-2-2-2-200002-2000000-2-2002200000000000000
χ1022222222222222222-2-22-2-222-2-2-2-20000-220000002200-2-200000000000000
χ112222222222222222-22-2-22-2-2-2-2-222200-20022000000-2-20000000000000000
χ122222222222222222-22-2-22-2-2-2-2-222-200200-2-2000000220000000000000000
χ132222222222222222-2-22-2-22-2-222-2-202-20000022-2-200000000000000000000
χ142222222222222222-2-22-2-22-2-222-2-20-2200000-2-22200000000000000000000
χ1522222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ1622222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-12-2-22-2-2-1-1111111-1-11100000000000000
χ1722222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-222-2-2-211-1-1-1-111111100000000000000
χ1822222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-2-2-2-222111111-1-111-1-100000000000000
χ1922222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1111100002-2−i3i3−i3i3−i3i311−i3i3-1-100000000000000
χ2022222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1111100002-2i3−i3i3−i3i3−i311i3−i3-1-100000000000000
χ2122222222-1-1-1-1-1-1-1-12-2-22-2-2-1-111110000-22−i3i3i3−i3i3−i3-1-1−i3i31100000000000000
χ2222222222-1-1-1-1-1-1-1-12-2-22-2-2-1-111110000-22i3−i3−i3i3−i3i3-1-1i3−i31100000000000000
χ2322222222-1-1-1-1-1-1-1-1-22-2-22-21111-1-1200-200-1-1−i3i3i3−i3−i3i311−i3i300000000000000
χ2422222222-1-1-1-1-1-1-1-1-22-2-22-21111-1-1200-200-1-1i3−i3−i3i3i3−i311i3−i300000000000000
χ2522222222-1-1-1-1-1-1-1-1-22-2-22-21111-1-1-20020011−i3i3i3−i3i3−i3-1-1i3−i300000000000000
χ2622222222-1-1-1-1-1-1-1-1-22-2-22-21111-1-1-20020011i3−i3−i3i3−i3i3-1-1−i3i300000000000000
χ2722222222-1-1-1-1-1-1-1-1-2-22-2-2211-1-11102-2000−i3i3-1-111i3−i3i3−i3−i3i300000000000000
χ2822222222-1-1-1-1-1-1-1-1-2-22-2-2211-1-11102-2000i3−i3-1-111−i3i3−i3i3i3−i300000000000000
χ2922222222-1-1-1-1-1-1-1-1-2-22-2-2211-1-1110-22000−i3i311-1-1−i3i3i3−i3i3−i300000000000000
χ3022222222-1-1-1-1-1-1-1-1-2-22-2-2211-1-1110-22000i3−i311-1-1i3−i3−i3i3−i3i300000000000000
χ312-2-22-2-2222-2-22-2-222222-2-2-22-22-22-200000000000000000000002i2i−2i−2i000000
χ322-2-22-2-2222-2-22-2-222222-2-2-22-22-22-20000000000000000000000−2i−2i2i2i000000
χ332-2-22-2-2222-2-22-2-2222-2-2-2222-2-22-220000000000000000000000000022-2-200
χ342-2-22-2-2222-2-22-2-2222-2-2-2222-2-22-2200000000000000000000000000-2-22200
χ352-2-22-2-2222-2-22-2-222-22-22-22-22-222-200000000000000000022-2-20000000000
χ362-2-22-2-2222-2-22-2-222-22-22-22-22-222-2000000000000000000-2-2220000000000
χ372-2-22-2-2222-2-22-2-222-2-2222-2-222-2-220000000000000000000000000000002-2
χ382-2-22-2-2222-2-22-2-222-2-2222-2-222-2-22000000000000000000000000000000-22
χ39444-4-4-4-44444-4-4-44-400000000000000000000000000000000002i−2i2i−2i000000
χ40444-4-4-4-44444-4-4-44-40000000000000000000000000000000000−2i2i−2i2i000000
χ4144-444-4-4-444-444-4-4-40000000000000000000000000000002-22-20000000000
χ4244-444-4-4-444-444-4-4-4000000000000000000000000000000-22-220000000000
χ4344-4-4-444-444-4-4-44-44000000000000000000000000000000000000002i−2i2i−2i00
χ4444-4-4-444-444-4-4-44-4400000000000000000000000000000000000000−2i2i−2i2i00
χ454-444-44-4-44-444-44-4-40000000000000000000000000000002-2-220000000000
χ464-444-44-4-44-444-44-4-4000000000000000000000000000000-222-20000000000
χ474-44-44-44-44-44-44-4-44000000000000000000000000000000000000002i−2i−2i2i00
χ484-44-44-44-44-44-44-4-4400000000000000000000000000000000000000−2i2i2i−2i00
χ494-4-44-4-444-222-222-2-2444-4-4-4-22-22-2200000000000000000000000000000000
χ504-4-44-4-444-222-222-2-24-4-4-444-222-22-200000000000000000000000000000000
χ514-4-44-4-444-222-222-2-2-44-44-442-22-2-2200000000000000000000000000000000
χ524-4-44-4-444-222-222-2-2-4-4444-42-2-222-200000000000000000000000000000000
χ534-4-4-444-444-4-4-4444-400000000000000000000000000000000002-2-22000000
χ544-4-4-444-444-4-4-4444-40000000000000000000000000000000000-222-2000000
χ55888-8-8-8-88-4-4-4444-4400000000000000000000000000000000000000000000
χ5688-888-8-8-8-4-44-4-444400000000000000000000000000000000000000000000
χ5788-8-8-888-8-4-4444-44-400000000000000000000000000000000000000000000
χ588-888-88-8-8-44-4-44-44400000000000000000000000000000000000000000000
χ598-88-88-88-8-44-44-444-400000000000000000000000000000000000000000000
χ608-8-8-888-88-4444-4-4-4400000000000000000000000000000000000000000000

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