Finite Group Databasebeta

← Group #315345

Character table — Group #315345

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888844444444444488888888888888888844882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-11
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1
χ71111111111111111111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1
χ81111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11
χ9111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ10111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111111-1-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-11-1
χ172222222222-2-22-2-22-2-222220000-2-2-2-200000022-2-200000000000000000000-22000000
χ182222222222-2-22-2-22-2-222220000-2-2-2-2000000-2-222000000000000000000002-2000000
χ192222222222-2-22-2-22-2-2-2-2-2-20000222200000022-2-2000000000000000000002-2000000
χ202222222222-2-22-2-22-2-2-2-2-2-200002222000000-2-22200000000000000000000-22000000
χ2122222222-2-222-222-2-2-20000222200002222-2-20000-2-2-2-2000000000000000000000000
χ2222222222-2-222-222-2-2-2000022220000-2-2-2-222000022-2-2000000000000000000000000
χ2322222222-2-222-222-2-2-20000-2-2-2-2000022-2-2220000-2-222000000000000000000000000
χ2422222222-2-222-222-2-2-20000-2-2-2-20000-2-222-2-200002222000000000000000000000000
χ25222-2-2-2-222-2-2-2222-2-2200002i2i−2i−2i00000000000000002i−2i22-2-200002i2i−2i−2i000000000000
χ26222-2-2-2-222-2-2-2222-2-2200002i2i−2i−2i00000000000000002i−2i-2-2220000−2i−2i2i2i000000000000
χ27222-2-2-2-222-2-2-2222-2-220000−2i−2i2i2i0000000000000000−2i2i22-2-20000−2i−2i2i2i000000000000
χ28222-2-2-2-222-2-2-2222-2-220000−2i−2i2i2i0000000000000000−2i2i-2-22200002i2i−2i−2i000000000000
χ29222-2-2-2-22-2222-2-2-22-2222-2-2000022-2-20000000000000000002i2i−2i−2i00000000002i−2i0000
χ30222-2-2-2-22-2222-2-2-22-2222-2-2000022-2-2000000000000000000−2i−2i2i2i0000000000−2i2i0000
χ31222-2-2-2-22-2222-2-2-22-22-2-2220000-2-2220000000000000000002i2i−2i−2i0000000000−2i2i0000
χ32222-2-2-2-22-2222-2-2-22-22-2-2220000-2-222000000000000000000−2i−2i2i2i00000000002i−2i0000
χ33222-2-2-2-22-22-2-2-22222-222-2-22i2i−2i−2i-2-222000000000000−2i2i0000000000002i2i−2i−2i00000000
χ34222-2-2-2-22-22-2-2-22222-222-2-2−2i−2i2i2i-2-2220000000000002i−2i000000000000−2i−2i2i2i00000000
χ35222-2-2-2-22-22-2-2-22222-2-2-2222i2i−2i−2i22-2-2000000000000−2i2i000000000000−2i−2i2i2i00000000
χ36222-2-2-2-22-22-2-2-22222-2-2-222−2i−2i2i2i22-2-20000000000002i−2i0000000000002i2i−2i−2i00000000
χ372-222-22-2-2002-202-2000i2−i2i2−i22-22-2i2−i2i2−i200002i−2i00002i−2i002−22−200002−22−2i2−i2i2−i200000000
χ382-222-22-2-2002-202-2000i2−i2i2−i22-22-2i2−i2i2−i20000−2i2i0000−2i2i00−22−220000−22−22i2−i2i2−i200000000
χ392-222-22-2-2002-202-2000i2−i2i2−i2-22-22i2−i2i2−i200002i−2i0000−2i2i002−22−20000−22−22−i2i2−i2i200000000
χ402-222-22-2-2002-202-2000i2−i2i2−i2-22-22i2−i2i2−i20000−2i2i00002i−2i00−22−2200002−22−2−i2i2−i2i200000000
χ412-222-22-2-2002-202-2000−i2i2−i2i22-22-2−i2i2−i2i200002i−2i00002i−2i00−22−220000−22−22−i2i2−i2i200000000
χ422-222-22-2-2002-202-2000−i2i2−i2i22-22-2−i2i2−i2i20000−2i2i0000−2i2i002−22−200002−22−2−i2i2−i2i200000000
χ432-222-22-2-2002-202-2000−i2i2−i2i2-22-22−i2i2−i2i200002i−2i0000−2i2i00−22−2200002−22−2i2−i2i2−i200000000
χ442-222-22-2-2002-202-2000−i2i2−i2i2-22-22−i2i2−i2i20000−2i2i00002i−2i002−22−20000−22−22i2−i2i2−i200000000
χ452-22-22-22-200-2202-2000i2−i2−i2i22i−2i−2i2i−i2i2i2−i22-22i−2i00000000002−2−220000i2−i2−i2i2−222−200000000
χ462-22-22-22-200-2202-2000i2−i2−i2i22i−2i−2i2i−i2i2i2−i2-22−2i2i0000000000−222−20000−i2i2i2−i2−222−200000000
χ472-22-22-22-200-2202-2000i2−i2−i2i2−2i2i2i−2i−i2i2i2−i22-2−2i2i0000000000−222−20000i2−i2−i2i22−2−2200000000
χ482-22-22-22-200-2202-2000i2−i2−i2i2−2i2i2i−2i−i2i2i2−i2-222i−2i00000000002−2−220000−i2i2i2−i22−2−2200000000
χ492-22-22-22-200-2202-2000−i2i2i2−i22i−2i−2i2ii2−i2−i2i22-22i−2i0000000000−222−20000−i2i2i2−i22−2−2200000000
χ502-22-22-22-200-2202-2000−i2i2i2−i22i−2i−2i2ii2−i2−i2i2-22−2i2i00000000002−2−220000i2−i2−i2i22−2−2200000000
χ512-22-22-22-200-2202-2000−i2i2i2−i2−2i2i2i−2ii2−i2−i2i22-2−2i2i00000000002−2−220000−i2i2i2−i2−222−200000000
χ522-22-22-22-200-2202-2000−i2i2i2−i2−2i2i2i−2ii2−i2−i2i2-222i−2i0000000000−222−20000i2−i2−i2i2−222−200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ54444-4-4-4-444-4444-4-4-44-400000000000000000000000000000000000000000000000000
χ5544-444-4-4-44400-400-40000000000000000000000000000000022−2222−220000000000000000
χ5644-444-4-4-44400-400-400000000000000000000000000000000−2222−22220000000000000000
χ5744-444-4-4-4-4-400400400000000000000000000004i−4i0000000000000000000000000000
χ5844-444-4-4-4-4-40040040000000000000000000000−4i4i0000000000000000000000000000
χ5944-4-4-444-44-400-4004000000000000000000004i−4i000000000000000000000000000000
χ6044-4-4-444-44-400-400400000000000000000000−4i4i000000000000000000000000000000
χ6144-4-4-444-4-4400400-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ6244-4-4-444-4-4400400-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ634-444-44-4-400-440-440002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000000000
χ644-444-44-4-400-440-44000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000000000
χ654-44-44-44-4004-40-440002i2−2i2−2i22i200002i2−2i2−2i22i200000000000000000000000000000000000000
χ664-44-44-44-4004-40-44000−2i22i22i2−2i20000−2i22i22i2−2i200000000000000000000000000000000000000
χ678-8-88-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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