Finite Group Databasebeta

← Group #278309

Character table — Group #278309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882244444444488884444888888888888888888888888844882288
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1111-1-1-1-111111111-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1
χ71111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-111
χ9111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1111-11-1
χ10111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-111-11-11
χ11111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-111-1-1-11-11
χ12111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-1-1-1111111-1-11-11-1
χ13111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11111-1-1-1-1-1-1111111-1-1-111-1
χ14111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-111-1-1111111-1-1-1-111-1-11-1-11
χ15111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-11111-1-1111-1-11
χ16111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1111111-1-1-1-1-1-111-111-1
χ1722222222-222-222222222-2-2-2-2-2-2-222-2-200002200000000-2-2-200000000000000000000
χ1822222222-222-22222-2-2-2-2-2-2-2222222-2-20000-2-200000000-22200000000000000000000
χ1922222222-222-2-2-2-2-22222-2-2-2-2-2-2-2-2-2220000-2-20000000022200000000000000000000
χ2022222222-222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222000022000000002-2-200000000000000000000
χ212222-2-22-222-22000022-2-22-2-222-2-2000000000022-2-200000000000000000002-2000000
χ222222-2-22-222-22000022-2-22-2-222-2-20000000000-2-2220000000000000000000-22000000
χ232222-2-22-222-220000-2-2222-2-2-2-222000000000022-2-20000000000000000000-22000000
χ242222-2-22-222-220000-2-2222-2-2-2-2220000000000-2-22200000000000000000002-2000000
χ252222-2-22-2-22-2-2000022-2-2-222-2-22200002i2i−2i−2i0000000000000000000000000002i−2i0000
χ262222-2-22-2-22-2-2000022-2-2-222-2-2220000−2i−2i2i2i000000000000000000000000000−2i2i0000
χ272222-2-22-2-22-2-20000-2-222-22222-2-200002i2i−2i−2i000000000000000000000000000−2i2i0000
χ282222-2-22-2-22-2-20000-2-222-22222-2-20000−2i−2i2i2i0000000000000000000000000002i−2i0000
χ292222-2-2-222-22222220000-22-20000-2-22200000000002222-200-2-2-2-20000000000000000
χ302222-2-2-222-22222220000-22-20000-2-2220000000000-2-2-2-2-20022220000000000000000
χ312222-2-2-222-222-2-2-2-20000-22-2000022-2-2000000000022-2-2200-2-2220000000000000000
χ322222-2-2-222-222-2-2-2-20000-22-2000022-2-20000000000-2-22220022-2-20000000000000000
χ332222-2-2-22-2-22-2222200002-220000-2-2-2-20000000000000020000002i2i−2i−2i2i2i−2i−2i00000000
χ342222-2-2-22-2-22-2222200002-220000-2-2-2-2000000000000002000000−2i−2i2i2i−2i−2i2i2i00000000
χ352222-2-2-22-2-22-2-2-2-2-200002-220000222200000000000000-20000002i2i−2i−2i−2i−2i2i2i00000000
χ362222-2-2-22-2-22-2-2-2-2-200002-220000222200000000000000-2000000−2i−2i2i2i2i2i−2i−2i00000000
χ3722-2-22-2-2202-2022-2-22-22-200000002-20000002-20000i2−i2i2−i2000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ3822-2-22-2-2202-2022-2-22-22-200000002-20000002-20000−i2i2−i2i2000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ3922-2-22-2-2202-2022-2-2-22-2200000002-2000000-220000i2−i2i2−i2000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ4022-2-22-2-2202-2022-2-2-22-2200000002-2000000-220000−i2i2−i2i2000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ4122-2-22-2-2202-20-2-2222-22-20000000-22000000-220000i2−i2−i2i2000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ4222-2-22-2-2202-20-2-2222-22-20000000-22000000-220000−i2i2i2−i2000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ4322-2-22-2-2202-20-2-222-22-220000000-220000002-20000i2−i2−i2i2000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ4422-2-22-2-2202-20-2-222-22-220000000-220000002-20000−i2i2i2−i2000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ4522-2-2-22220-2-2022-2-200000002i−2i2i−2i-22000000000000i2−i2i2−i202i−2i−i2i2−i2i22−2−222−2−2200000000
χ4622-2-2-22220-2-2022-2-200000002i−2i2i−2i-22000000000000−i2i2−i2i202i−2ii2−i2i2−i2−222−2−222−200000000
χ4722-2-2-22220-2-2022-2-20000000−2i2i−2i2i-22000000000000i2−i2i2−i20−2i2i−i2i2−i2i2−222−2−222−200000000
χ4822-2-2-22220-2-2022-2-20000000−2i2i−2i2i-22000000000000−i2i2−i2i20−2i2ii2−i2i2−i22−2−222−2−2200000000
χ4922-2-2-22220-2-20-2-22200000002i−2i2i−2i2-2000000000000i2−i2−i2i20−2i2i−i2i2i2−i22−2−22−222−200000000
χ5022-2-2-22220-2-20-2-22200000002i−2i2i−2i2-2000000000000−i2i2i2−i20−2i2ii2−i2−i2i2−222−22−2−2200000000
χ5122-2-2-22220-2-20-2-2220000000−2i2i−2i2i2-2000000000000i2−i2−i2i202i−2i−i2i2i2−i2−222−22−2−2200000000
χ5222-2-2-22220-2-20-2-2220000000−2i2i−2i2i2-2000000000000−i2i2i2−i202i−2ii2−i2−i2i22−2−22−222−200000000
χ53444444-4-44-4-4400000000-4-44000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40000000044-4000000000000000000000000000000000000000000000
χ5544-4-44-44-40-440000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ5644-4-44-44-40-44000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ5744-4-4-44-4-4044000004-4-44000000000000000000000000000000000000000000000000
χ5844-4-4-44-4-404400000-444-4000000000000000000000000000000000000000000000000
χ594-44-40000400-422−2222−22000000000000022−222i−2i2i−2i00002i2−2i2000000000000000000000000000
χ604-44-40000400-422−2222−22000000000000022−22−2i2i−2i2i0000−2i22i2000000000000000000000000000
χ614-44-40000400-4−2222−22220000000000000−22222i−2i2i−2i0000−2i22i2000000000000000000000000000
χ624-44-40000400-4−2222−22220000000000000−2222−2i2i−2i2i00002i2−2i2000000000000000000000000000
χ634-44-40000-400422−2222−220000000000000−22222-2-220022−2200000000000000000000000000000
χ644-44-40000-400422−2222−220000000000000−2222-222-200−222200000000000000000000000000000
χ654-44-40000-4004−2222−2222000000000000022−222-2-2200−222200000000000000000000000000000
χ664-44-40000-4004−2222−2222000000000000022−22-222-20022−2200000000000000000000000000000
χ678-8-880000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-8-8800000000−424242−420000000000000000000000000000000000000000000000000000

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