Finite Group Databasebeta

← Group #311368

Character table — Group #311368

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-111-11
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-111-1-11-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-11-1-11111-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111111-111-1-1-1-111-11
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1111-1-111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-111111-1-1-111-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-1111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-1-11111-1-1-11
χ172222222222-2-22-2-222222-2-20000000022-2-2-2-20000-2-200000000220000000000000000
χ182222222222-2-22-2-222222-2-200000000-2-2-2-22200002200000000-2-20000000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-2000000002222-2-200002200000000-2-20000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-200000000-2-222220000-2-200000000220000000000000000
χ2122222222-2-222-222-20000-2-22222-2-2-2-200000022220000000000000000-2-20000000000
χ2222222222-2-222-222-20000-2-22222-2-2-2-2000000-2-2-2-20000000000000000220000000000
χ2322222222-2-222-222-20000-2-2-2-2-2-2222200000022-2-200000000000000002-20000000000
χ2422222222-2-222-222-20000-2-2-2-2-2-22222000000-2-2220000000000000000-220000000000
χ25222-2-2-2-222-2-2-2222-20000-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000002i−2i2-2000000
χ26222-2-2-2-222-2-2-2222-20000-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i-22000000
χ27222-2-2-2-222-2-2-2222-20000-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i-22000000
χ28222-2-2-2-222-2-2-2222-20000-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i2-2000000
χ29222-2-2-2-22-2222-2-2-222i2i−2i−2i-2200000000002i−2i0000000000002i2i−2i−2i0022-2-2000000000000
χ30222-2-2-2-22-2222-2-2-222i2i−2i−2i-2200000000002i−2i000000000000−2i−2i2i2i00-2-222000000000000
χ31222-2-2-2-22-2222-2-2-22−2i−2i2i2i-220000000000−2i2i0000000000002i2i−2i−2i00-2-222000000000000
χ32222-2-2-2-22-2222-2-2-22−2i−2i2i2i-220000000000−2i2i000000000000−2i−2i2i2i0022-2-2000000000000
χ33222-2-2-2-22-22-2-2-22222i2i−2i−2i2-22i2i−2i−2i−2i−2i2i2i00−2i2i0000000022-2-20000000000000000000000
χ34222-2-2-2-22-22-2-2-22222i2i−2i−2i2-2−2i−2i2i2i2i2i−2i−2i00−2i2i00000000-2-2220000000000000000000000
χ35222-2-2-2-22-22-2-2-2222−2i−2i2i2i2-22i2i−2i−2i−2i−2i2i2i002i−2i00000000-2-2220000000000000000000000
χ36222-2-2-2-22-22-2-2-2222−2i−2i2i2i2-2−2i−2i2i2i2i2i−2i−2i002i−2i0000000022-2-20000000000000000000000
χ3722-222-2-2-2-2-20020022-22-2002−22−22−22−200002i−2i00002i−2i2−22−2i2−i2i2−i200i2−i2i2−i2000000000000
χ3822-222-2-2-2-2-20020022-22-2002−22−22−22−20000−2i2i0000−2i2i2−22−2−i2i2−i2i200−i2i2−i2i2000000000000
χ3922-222-2-2-2-2-20020022-22-200−22−22−22−2200002i−2i00002i−2i−22−22−i2i2−i2i200−i2i2−i2i2000000000000
χ4022-222-2-2-2-2-20020022-22-200−22−22−22−220000−2i2i0000−2i2i−22−22i2−i2i2−i200i2−i2i2−i2000000000000
χ4122-222-2-2-2-2-2002002-22-22002−22−22−22−200002i−2i0000−2i2i−22−22i2−i2i2−i200−i2i2−i2i2000000000000
χ4222-222-2-2-2-2-2002002-22-22002−22−22−22−20000−2i2i00002i−2i−22−22−i2i2−i2i200i2−i2i2−i2000000000000
χ4322-222-2-2-2-2-2002002-22-2200−22−22−22−2200002i−2i0000−2i2i2−22−2−i2i2−i2i200i2−i2i2−i2000000000000
χ4422-222-2-2-2-2-2002002-22-2200−22−22−22−220000−2i2i00002i−2i2−22−2i2−i2i2−i200−i2i2−i2i2000000000000
χ4522-2-2-222-22-200-20022i−2i−2i2i00i2−i2−i2i2−i2i2i2−i22i−2i00000000002−2−222−2−222-2−i2i2i2−i2000000000000
χ4622-2-2-222-22-200-20022i−2i−2i2i00i2−i2−i2i2−i2i2i2−i2−2i2i00000000002−2−22−222−2-22i2−i2−i2i2000000000000
χ4722-2-2-222-22-200-20022i−2i−2i2i00−i2i2i2−i2i2−i2−i2i22i−2i0000000000−222−2−222−22-2i2−i2−i2i2000000000000
χ4822-2-2-222-22-200-20022i−2i−2i2i00−i2i2i2−i2i2−i2−i2i2−2i2i0000000000−222−22−2−22-22−i2i2i2−i2000000000000
χ4922-2-2-222-22-200-2002−2i2i2i−2i00i2−i2−i2i2−i2i2i2−i22i−2i0000000000−222−22−2−22-22i2−i2−i2i2000000000000
χ5022-2-2-222-22-200-2002−2i2i2i−2i00i2−i2−i2i2−i2i2i2−i2−2i2i0000000000−222−2−222−22-2−i2i2i2−i2000000000000
χ5122-2-2-222-22-200-2002−2i2i2i−2i00−i2i2i2−i2i2−i2−i2i22i−2i00000000002−2−22−222−2-22−i2i2i2−i2000000000000
χ5222-2-2-222-22-200-2002−2i2i2i−2i00−i2i2i2−i2i2−i2−i2i2−2i2i00000000002−2−222−2−222-2i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-4-4-4-444-4444-4-4-400004-40000000000000000000000000000000000000000000000
χ5544-444-4-4-44400-400-400000022−2222−22−2222−222200000000000000000000000000000000000000
χ5644-444-4-4-44400-400-4000000−2222−222222−2222−2200000000000000000000000000000000000000
χ5744-4-4-444-4-4400400-40000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5844-4-4-444-4-4400400-4000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-444-44-4-4004-404-40000000000000000000004i−4i000000000000000000000000000000
χ604-444-44-4-4004-404-4000000000000000000000−4i4i000000000000000000000000000000
χ614-444-44-4-400-440-4400000000000000000000000000000000000000000000000002i2−2i200
χ624-444-44-4-400-440-440000000000000000000000000000000000000000000000000−2i22i200
χ634-44-44-44-4004-40-44000000000000000000000000000000000000000000000002i2−2i20000
χ644-44-44-44-4004-40-4400000000000000000000000000000000000000000000000−2i22i20000
χ654-44-44-44-400-4404-4000000000000000000000004i−4i0000000000000000000000000000
χ664-44-44-44-400-4404-400000000000000000000000−4i4i0000000000000000000000000000
χ678-8-88-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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