Finite Group Databasebeta

← Group #288173

Character table — Group #288173

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888224444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-111-1-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-111111-1-1-11
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11-111-1-111-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-11-1-111-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11-11111-1-11-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-111-11-1-1-1-111-11
χ172222222222-2-2-222-22222-2-20000000022-2-20000-2-2000022-2-200000000000000000000
χ182222222222-2-2-222-22222-2-200000000-2-2-2-20000220000-2-22200000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-20000000022220000-2-20000-2-22200000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-200000000-2-222000022000022-2-200000000000000000000
χ2122222222-2-2222-2-220000-2-22222-2-2-2-20000222200000000000000000000-2-200000000
χ2222222222-2-2222-2-220000-2-22222-2-2-2-20000-2-2-2-2000000000000000000002200000000
χ2322222222-2-2222-2-220000-2-2-2-2-2-22222000022-2-200000000000000000000-2200000000
χ2422222222-2-2222-2-220000-2-2-2-2-2-222220000-2-222000000000000000000002-200000000
χ25222-22-2-2-22-20002-2022-2-200i2i2−i2−i2i2i2−i2−i2000000002i−2ii2i2−i2−i2002i−2i22−2−222−2−2000000000000
χ26222-22-2-2-22-20002-2022-2-200i2i2−i2−i2i2i2−i2−i200000000−2i2ii2i2−i2−i200−2i2i−2−222−2−222000000000000
χ27222-22-2-2-22-20002-2022-2-200−i2−i2i2i2−i2−i2i2i2000000002i−2i−i2−i2i2i2002i−2i−2−222−2−222000000000000
χ28222-22-2-2-22-20002-2022-2-200−i2−i2i2i2−i2−i2i2i200000000−2i2i−i2−i2i2i200−2i2i22−2−222−2−2000000000000
χ29222-22-2-2-22-20002-20-2-22200i2i2−i2−i2i2i2−i2−i2000000002i−2i−i2−i2i2i200−2i2i22−2−2−2−222000000000000
χ30222-22-2-2-22-20002-20-2-22200i2i2−i2−i2i2i2−i2−i200000000−2i2i−i2−i2i2i2002i−2i−2−22222−2−2000000000000
χ31222-22-2-2-22-20002-20-2-22200−i2−i2i2i2−i2−i2i2i2000000002i−2ii2i2−i2−i200−2i2i−2−22222−2−2000000000000
χ32222-22-2-2-22-20002-20-2-22200−i2−i2i2i2−i2−i2i2i200000000−2i2ii2i2−i2−i2002i−2i22−2−2−2−222000000000000
χ3322-22-22-2-22-2000-2202i−2i2i−2i00i2−i2i2−i2i2−i2i2−i22-2000000002−22−22i−2i00i2−i2i2−i22−22−2000000000000
χ3422-22-22-2-22-2000-2202i−2i2i−2i00i2−i2i2−i2i2−i2i2−i2-22000000002−22−2−2i2i00−i2i2−i2i2−22−22000000000000
χ3522-22-22-2-22-2000-2202i−2i2i−2i00−i2i2−i2i2−i2i2−i2i22-200000000−22−222i−2i00−i2i2−i2i2−22−22000000000000
χ3622-22-22-2-22-2000-2202i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2-2200000000−22−22−2i2i00i2−i2i2−i22−22−2000000000000
χ3722-22-22-2-22-2000-220−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i22-200000000−22−22−2i2i00i2−i2i2−i2−22−22000000000000
χ3822-22-22-2-22-2000-220−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2-2200000000−22−222i−2i00−i2i2−i2i22−22−2000000000000
χ3922-22-22-2-22-2000-220−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i22-2000000002−22−2−2i2i00−i2i2−i2i22−22−2000000000000
χ4022-22-22-2-22-2000-220−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2-22000000002−22−22i−2i00i2−i2i2−i2−22−22000000000000
χ4122-2-2-2-222222-22-2-2-22i−2i−2i2i-2200000000002i−2i000000000000002i−2i−2i2i2-2-22000000000000
χ4222-2-2-2-222222-22-2-2-22i−2i−2i2i-2200000000002i−2i00000000000000−2i2i2i−2i-222-2000000000000
χ4322-2-2-2-222222-22-2-2-2−2i2i2i−2i-220000000000−2i2i000000000000002i−2i−2i2i-222-2000000000000
χ4422-2-2-2-222222-22-2-2-2−2i2i2i−2i-220000000000−2i2i00000000000000−2i2i2i−2i2-2-22000000000000
χ4522-2-2-2-22222-22-2-2-222i−2i−2i2i2-22-2-222-2-2200−2i2i000000−2i2i2i−2i000000000000000000000000
χ4622-2-2-2-22222-22-2-2-222i−2i−2i2i2-2-222-2-222-200−2i2i0000002i−2i−2i2i000000000000000000000000
χ4722-2-2-2-22222-22-2-2-22−2i2i2i−2i2-22-2-222-2-22002i−2i0000002i−2i−2i2i000000000000000000000000
χ4822-2-2-2-22222-22-2-2-22−2i2i2i−2i2-2-222-2-222-2002i−2i000000−2i2i2i−2i000000000000000000000000
χ4922-2-2-2-222-2-2-22-22220000-222-2-22-222-2000000000000000000000000002-2002-2000000
χ5022-2-2-2-222-2-2-22-22220000-222-2-22-222-200000000000000000000000000-2200-22000000
χ5122-2-2-2-222-2-2-22-22220000-22-222-22-2-22000000000000000000000000002-200-22000000
χ5222-2-2-2-222-2-2-22-22220000-22-222-22-2-2200000000000000000000000000-22002-2000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-44-4-4-4-44000-4400000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ55444-44-4-4-4-44000-440000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-44-44-4-4-440004-400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ5744-44-44-4-4-440004-40000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ5844-4-4-4-444-4-44-4444-400004-40000000000000000000000000000000000000000000000
χ594-444-4-4-440044-400-40000000000000000004i−4i00000000000000000000000000000000
χ604-444-4-4-440044-400-4000000000000000000−4i4i00000000000000000000000000000000
χ614-444-4-4-4400-4-44004000000000000000000000000000000000000000000000022−220000
χ624-444-4-4-4400-4-440040000000000000000000000000000000000000000000000−22220000
χ634-4-4-444-44004-4-400400000000000000000000000000000000000000000000000022−2200
χ644-4-4-444-44004-4-4004000000000000000000000000000000000000000000000000−222200
χ654-4-4-444-4400-44400-4000000000000000000004-4000000000000000000000000000000
χ664-4-4-444-4400-44400-400000000000000000000-44000000000000000000000000000000
χ678-88-8-888-8000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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