Finite Group Databasebeta

← Group #10697946

Character table — Group #10697946

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222222222444444444488881212121212121212161616161616161616161616161616161616484848484848
order122234444446662444121212121212612121244444444444488121212121212121224242424248888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-11-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111
χ92222222-2-222222-2-2-222222-2-2-2-2-22000000000000000000000000002-20000
χ102222222-2-222222-2-2-222222-2-2-2-2-2200000000000000000000000000-220000
χ11222222-2222-2222-22-2-222-2-222-22-2-200000000020-200002200-2-20000000000
χ12222222-2222-2222-22-2-222-2-222-22-2-2000000000-2020000-2-200220000000000
χ13222222-2-2-22-22222-22-222-2-2-2-22-22-200000000000000000000000000002-200
χ14222222-2-2-22-22222-22-222-2-2-2-22-22-20000000000000000000000000000-2200
χ1522222-2222-22222-2-22-2-2-22222-2-22-20000000020-20002200-2-2000000000000
χ1622222-2222-22222-2-22-2-2-22222-2-22-200000000-202000-2-20022000000000000
χ1722222-22-2-2-2222222-2-2-2-222-2-222-2-20000000000000000000000000000002-2
χ1822222-22-2-2-2222222-2-2-2-222-2-222-2-2000000000000000000000000000000-22
χ1922222-2-222-2-22222-2-22-2-2-2-2222-2-220000000000002-20000000022-2-2000000
χ2022222-2-222-2-22222-2-22-2-2-2-2222-2-22000000000000-2200000000-2-222000000
χ2122222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ2222222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ232222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-100000000222222-1-1-1-1-1-1-1-1-1-1-1-1000000
χ242222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002-22-2-2-2-1-111-1-1111111000000
χ252222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-22-22-2-211-1-111-1-11111000000
χ262222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-22211111111-1-1-1-1000000
χ272222-12-2222-2-1-1-1-22-2-2-1-111-1-11-11100000000020-200−i3i3-1-1−i3i311−i3i3−i3i3000000
χ282222-12-2222-2-1-1-1-22-2-2-1-111-1-11-11100000000020-200i3−i3-1-1i3−i311i3−i3i3−i3000000
χ292222-12-2222-2-1-1-1-22-2-2-1-111-1-11-111000000000-20200−i3i311−i3i3-1-1i3−i3i3−i3000000
χ302222-12-2222-2-1-1-1-22-2-2-1-111-1-11-111000000000-20200i3−i311i3−i3-1-1−i3i3−i3i3000000
χ312222-1-2222-22-1-1-1-2-22-211-1-1-1-111-110000000020-2000-1-1−i3i311−i3i3−i3i3i3−i3000000
χ322222-1-2222-22-1-1-1-2-22-211-1-1-1-111-110000000020-2000-1-1i3−i311i3−i3i3−i3−i3i3000000
χ332222-1-2222-22-1-1-1-2-22-211-1-1-1-111-1100000000-20200011−i3i3-1-1−i3i3i3−i3−i3i3000000
χ342222-1-2222-22-1-1-1-2-22-211-1-1-1-111-1100000000-20200011i3−i3-1-1i3−i3−i3i3i3−i3000000
χ352222-1-2-222-2-2-1-1-12-2-221111-1-1-111-10000000000002-2−i3i3−i3i3i3−i3i3−i3-1-111000000
χ362222-1-2-222-2-2-1-1-12-2-221111-1-1-111-10000000000002-2i3−i3i3−i3−i3i3−i3i3-1-111000000
χ372222-1-2-222-2-2-1-1-12-2-221111-1-1-111-1000000000000-22−i3i3i3−i3i3−i3−i3i311-1-1000000
χ382222-1-2-222-2-2-1-1-12-2-221111-1-1-111-1000000000000-22i3−i3−i3i3−i3i3i3−i311-1-1000000
χ394444-244-4-444-2-2-2-4-4-44-2-2-2-222222-200000000000000000000000000000000
χ404444-24-4-4-44-4-2-2-24-44-4-2-22222-22-2200000000000000000000000000000000
χ414444-2-44-4-4-44-2-2-244-4-422-2-222-2-22200000000000000000000000000000000
χ424444-2-4-4-4-4-4-4-2-2-2-44442222222-2-2-200000000000000000000000000000000
χ4344-4-4404000-44-4-40000004-400000022-2-222-2-2000000000000000000000000
χ4444-4-4404000-44-4-40000004-4000000-2-222-2-222000000000000000000000000
χ4544-4-440-400044-4-4000000-440000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ4644-4-440-400044-4-4000000-44000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ474-44-444000-40-44-400004-4000000002-22-22-22-2000000000000000000000000
χ484-44-444000-40-44-400004-400000000-22-22-22-22000000000000000000000000
χ494-44-44-400040-44-40000-44000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ504-44-44-400040-44-40000-4400000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ514-4-444004-400-4-44000000004-400002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ524-4-444004-400-4-44000000004-40000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ534-4-44400-4400-4-4400000000-4400002-2-222-2-22000000000000000000000000
χ544-4-44400-4400-4-4400000000-440000-222-2-222-2000000000000000000000000
χ5588-8-8-408000-8-444000000-4400000000000000000000000000000000000000
χ5688-8-8-40-80008-4440000004-400000000000000000000000000000000000000
χ578-88-8-48000-804-440000-440000000000000000000000000000000000000000
χ588-88-8-4-8000804-4400004-40000000000000000000000000000000000000000
χ598-8-88-4008-80044-400000000-44000000000000000000000000000000000000
χ608-8-88-400-880044-4000000004-4000000000000000000000000000000000000

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