Finite Group Databasebeta

← Group #10825716

Character table — Group #10825716

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222233334444444444666666888888888888888812121212161616161616161616161616242424242424242424242424
order12442223444612128888666888812121288888824444488888824242424224461212121212242424242424224444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-111-1-111-1-1-1-11-11-1-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-111-1-111111111-1-1-1-111-1-111-1-1-11-11-1-1-1-1-1-111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-11-1-11111-1-1
χ6111111111111111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-1-1-111-1-111
χ7111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111
χ8111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ911111111111111-1-1-1-11111111111-1-1-1-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-11-111111-1-111
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11-11-1111111-1-1
χ1311111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11-11-111-1-1-1-111
χ1411111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-11-1111-1-111-1-1
χ1511111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111111-1-111-1-1-1-1
χ1611111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111111
χ172222222-1222-1-1-10000-1-1-12222-1-1-1000000222222222222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-10000-1-1-12222-1-1-100000022-2-2-2-2-2-2-2-222-1-1-1-10000-1-111111111-1-1000000000000
χ192222222-1222-1-1-10000-1-1-12222-1-1-1000000-2-222-2-222-2-2-2-2-1-1-1-1000011-1-111-1-11111000000000000
χ202222222-1222-1-1-10000-1-1-12222-1-1-1000000-2-2-2-222-2-222-2-2-1-1-1-100001111-1-111-1-111000000000000
χ212222222-1222-1-1-10000-1-1-1-2-2-2-2-1-1-10000002222-2-2-2-222-2-211110000-1-1-1-11111-1-111000000000000
χ222222222-1222-1-1-10000-1-1-1-2-2-2-2-1-1-100000022-2-22222-2-2-2-211110000-1-111-1-1-1-11111000000000000
χ232222222-1222-1-1-10000-1-1-1-2-2-2-2-1-1-1000000-2-22222-2-2-2-2221111000011-1-1-1-11111-1-1000000000000
χ242222222-1222-1-1-10000-1-1-1-2-2-2-2-1-1-1000000-2-2-2-2-2-222222211110000111111-1-1-1-1-1-1000000000000
χ2522222-2-22-22-22222222-22-200002-2-222-2-2-2-200002-20000000000000000002-200000000000000002-2
χ2622222-2-22-22-22222222-22-200002-2-222-2-2-2-20000-22000000000000000000-220000000000000000-22
χ2722222-2-22-22-2222-2-2-2-2-22-200002-2-2-2-2222200002-20000000000000000002-20000000000000000-22
χ2822222-2-22-22-2222-2-2-2-2-22-200002-2-2-2-222220000-22000000000000000000-2200000000000000002-2
χ292222-22-22-2-222222222-2-220000-22-2-2-222-2-2002-20000000000000000002-200000000000000002-200
χ302222-22-22-2-222222222-2-220000-22-2-2-222-2-200-22000000000000000000-220000000000000000-2200
χ312222-22-22-2-22222-2-2-2-2-2-220000-22-222-2-222002-20000000000000000002-20000000000000000-2200
χ322222-22-22-2-22222-2-2-2-2-2-220000-22-222-2-22200-22000000000000000000-2200000000000000002-200
χ332222-2-2222-2-222222222-2-20000-2-22-2-2-2-22200000000002-20000000000000000002-200002-2000000
χ342222-2-2222-2-222222222-2-20000-2-22-2-2-2-2220000000000-22000000000000000000-220000-22000000
χ352222-2-2222-2-2222-2-2-2-22-2-20000-2-222222-2-200000000002-20000000000000000002-20000-22000000
χ362222-2-2222-2-2222-2-2-2-22-2-20000-2-222222-2-20000000000-22000000000000000000-2200002-2000000
χ3722-2-22222-2-2-22-2-22i2i−2i−2i2222i2i−2i−2i-2-2-22i−2i2i−2i2i−2i0000000000002i2i−2i−2i22-2-2000000000000000000000000
χ3822-2-22222-2-2-22-2-22i2i−2i−2i222−2i−2i2i2i-2-2-22i−2i2i−2i2i−2i000000000000−2i−2i2i2i-2-222000000000000000000000000
χ3922-2-22222-2-2-22-2-2−2i−2i2i2i2222i2i−2i−2i-2-2-2−2i2i−2i2i−2i2i0000000000002i2i−2i−2i-2-222000000000000000000000000
χ4022-2-22222-2-2-22-2-2−2i−2i2i2i222−2i−2i2i2i-2-2-2−2i2i−2i2i−2i2i000000000000−2i−2i2i2i22-2-2000000000000000000000000
χ4122-2-22-2-222-222-2-22i2i−2i−2i-22-20000-2222i−2i−2i2i−2i2i000000002i−2i0000000000000000002i−2i00020-200000000
χ4222-2-22-2-222-222-2-22i2i−2i−2i-22-20000-2222i−2i−2i2i−2i2i00000000−2i2i000000000000000000−2i2i000-20200000000
χ4322-2-22-2-222-222-2-2−2i−2i2i2i-22-20000-222−2i2i2i−2i2i−2i000000002i−2i0000000000000000002i−2i000-20200000000
χ4422-2-22-2-222-222-2-2−2i−2i2i2i-22-20000-222−2i2i2i−2i2i−2i00000000−2i2i000000000000000000−2i2i00020-200000000
χ4522-2-2-22-2222-22-2-22i2i−2i−2i-2-2200002-22−2i2i2i−2i−2i2i0000002i−2i0000000000000000002i−2i000020-2000000000
χ4622-2-2-22-2222-22-2-22i2i−2i−2i-2-2200002-22−2i2i2i−2i−2i2i000000−2i2i000000000000000000−2i2i0000-202000000000
χ4722-2-2-22-2222-22-2-2−2i−2i2i2i-2-2200002-222i−2i−2i2i2i−2i0000002i−2i0000000000000000002i−2i0000-202000000000
χ4822-2-2-22-2222-22-2-2−2i−2i2i2i-2-2200002-222i−2i−2i2i2i−2i000000−2i2i000000000000000000−2i2i000020-2000000000
χ4922-2-2-2-222-2222-2-22i2i−2i−2i2-2-2000022-2−2i2i−2i2i2i−2i2-20000000000000000002-200000000000000002i−2i0000
χ5022-2-2-2-222-2222-2-22i2i−2i−2i2-2-2000022-2−2i2i−2i2i2i−2i-22000000000000000000-220000000000000000−2i2i0000
χ5122-2-2-2-222-2222-2-2−2i−2i2i2i2-2-2000022-22i−2i2i−2i−2i2i2-20000000000000000002-20000000000000000−2i2i0000
χ5222-2-2-2-222-2222-2-2−2i−2i2i2i2-2-2000022-22i−2i2i−2i−2i2i-22000000000000000000-2200000000000000002i−2i0000
χ5344444-4-4-2-44-4-2-2-200002-220000-22200000000004-4000000000000000000-22000000000000000000
χ5444444-4-4-2-44-4-2-2-200002-220000-2220000000000-440000000000000000002-2000000000000000000
χ554444-44-4-2-4-44-2-2-2000022-200002-22000000004-4000000000000000000-2200000000000000000000
χ564444-44-4-2-4-44-2-2-2000022-200002-2200000000-440000000000000000002-200000000000000000000
χ574444-4-44-24-4-4-2-2-20000-222000022-200000000000000004-4000000000000000000-22000000000000
χ584444-4-44-24-4-4-2-2-20000-222000022-20000000000000000-440000000000000000002-2000000000000
χ5944-4-4444-2-4-4-4-2220000-2-2-24i4i−4i−4i222000000000000000000−2i−2i2i2i0000000000000000000000000000
χ6044-4-4444-2-4-4-4-2220000-2-2-2−4i−4i4i4i2220000000000000000002i2i−2i−2i0000000000000000000000000000
χ6144-4-44-4-4-24-44-22200002-2200002-2-2000000000000004i−4i000000000000000000−2i2i00000000000000
χ6244-4-44-4-4-24-44-22200002-2200002-2-200000000000000−4i4i0000000000000000002i−2i00000000000000
χ6344-4-4-44-4-244-4-222000022-20000-22-20000000000004i−4i000000000000000000−2i2i0000000000000000
χ6444-4-4-44-4-244-4-222000022-20000-22-2000000000000−4i4i0000000000000000002i−2i0000000000000000
χ6544-4-4-4-44-2-444-2220000-2220000-2-220000004-4000000000000000000-220000000000000000000000
χ6644-4-4-4-44-2-444-2220000-2220000-2-22000000-440000000000000000002-20000000000000000000000
χ674-44i−4i0004000-44i−4i4ζ−4ζ4ζ3−4ζ30002ζ−2ζ2ζ3−2ζ30000000000000000000002ζ−2ζ2ζ3−2ζ32-22i−2i000000000000000000000000
χ684-44i−4i0004000-44i−4i4ζ−4ζ4ζ3−4ζ3000−2ζ2ζ−2ζ32ζ3000000000000000000000−2ζ2ζ−2ζ32ζ3-22−2i2i000000000000000000000000
χ694-44i−4i0004000-44i−4i−4ζ4ζ−4ζ34ζ30002ζ−2ζ2ζ3−2ζ30000000000000000000002ζ−2ζ2ζ3−2ζ3-22−2i2i000000000000000000000000
χ704-44i−4i0004000-44i−4i−4ζ4ζ−4ζ34ζ3000−2ζ2ζ−2ζ32ζ3000000000000000000000−2ζ2ζ−2ζ32ζ32-22i−2i000000000000000000000000
χ714-4−4i4i0004000-4−4i4i4ζ3−4ζ34ζ−4ζ0002ζ3−2ζ32ζ−2ζ0000000000000000000002ζ3−2ζ32ζ−2ζ2-2−2i2i000000000000000000000000
χ724-4−4i4i0004000-4−4i4i4ζ3−4ζ34ζ−4ζ000−2ζ32ζ3−2ζ2ζ000000000000000000000−2ζ32ζ3−2ζ2ζ-222i−2i000000000000000000000000
χ734-4−4i4i0004000-4−4i4i−4ζ34ζ3−4ζ4ζ0002ζ3−2ζ32ζ−2ζ0000000000000000000002ζ3−2ζ32ζ−2ζ-222i−2i000000000000000000000000
χ744-4−4i4i0004000-4−4i4i−4ζ34ζ3−4ζ4ζ000−2ζ32ζ3−2ζ2ζ000000000000000000000−2ζ32ζ3−2ζ2ζ2-2−2i2i000000000000000000000000
χ758-88i−8i000-40004−4i4i00000004ζ−4ζ4ζ3−4ζ3000000000000000000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ768-88i−8i000-40004−4i4i0000000−4ζ4ζ−4ζ34ζ30000000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ778-8−8i8i000-400044i−4i00000004ζ3−4ζ34ζ−4ζ000000000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ788-8−8i8i000-400044i−4i0000000−4ζ34ζ3−4ζ4ζ0000000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.