Finite Group Databasebeta

← Group #72281697

Character table — Group #72281697

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size112222222224444444444444444444888888888888888888881616161616161616161616161616161632323232323232323232323232323232
order12222444488222222444444888888844444444888888888888161616161616161616161616161616164444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ9111-1-111-1-1111-1-1-111111-1-1-111-1-11-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−ii−ii−i11-1-111-1-1i−ii−i
χ10111-1-111-1-1111-1-1-111111-1-1-111-1-11-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i−ii−ii-1-111-1-111−ii−ii
χ11111-1-111-1-1111-1-1-111111-1-1-111-1-11-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiiii−ii−i11-1-1-1-111−ii−ii
χ12111-1-111-1-1111-1-1-111111-1-1-111-1-11-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii−ii−ii-1-11111-1-1i−ii−i
χ13111-1-111-1-1111-1-1-111111-1-1-111-1-11-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiiii−ii−i-1-111-1-111i−ii−i
χ14111-1-111-1-1111-1-1-111111-1-1-111-1-11-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−ii−ii11-1-111-1-1−ii−ii
χ15111-1-111-1-1111-1-1-111111-1-1-111-1-11-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−ii−ii−i-1-11111-1-1−ii−ii
χ16111-1-111-1-1111-1-1-111111-1-1-111-1-11-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i−ii−ii11-1-1-1-111i−ii−i
χ172222222222222-2-2-2-22-2-22-2-2222222200000000-2-2-2-2000000002222-2-2-2-2000000000000000000000000
χ182222222222222-2-2-2-22-2-22-2-2222222200000000-2-2-2-200000000-2-2-2-22222000000000000000000000000
χ1922222222222-2-22-22-2-22-2-22-2-2-2222-2-2000000002-22-200000000000000000000000000000000000022-2-2
χ2022222222222-2-22-22-2-22-2-22-2-2-2222-2-2000000002-22-2000000000000000000000000000000000000-2-222
χ2122222222222-2-2-22-22-2-22-2-22-2-2222-2-200000000-22-2200000000000000000000000022-2-2000000000000
χ2222222222222-2-2-22-22-2-22-2-22-2-2222-2-200000000-22-22000000000000000000000000-2-222000000000000
χ23222222222-2-2222222222222-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ24222222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ25222222222-2-222-2-2-2-22-2-22-2-2-2-2-2-2-2-2-200000000222200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ26222222222-2-222-2-2-2-22-2-22-2-2-2-2-2-2-2-2-20000000022220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ27222222222-2-2-2-22-22-2-22-2-22-222-2-2-22200000000-22-22000000000000000000000000000000002-22-20000
χ28222222222-2-2-2-22-22-2-22-2-22-222-2-2-22200000000-22-2200000000000000000000000000000000-22-220000
χ29222222222-2-2-2-2-22-22-2-22-2-2222-2-2-222000000002-22-200000000000000000000000000002-22-200000000
χ30222222222-2-2-2-2-22-22-2-22-2-2222-2-2-222000000002-22-20000000000000000000000000000-22-2200000000
χ3122222-2-2-2-200222-22-2-2-22-2-2200000000000000000002i2i−2i−2i2i2i−2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ3222222-2-2-2-200222-22-2-2-22-2-2200000000000000000002i2i−2i−2i2i2i−2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ3322222-2-2-2-200222-22-2-2-22-2-220000000000000000000−2i−2i2i2i−2i−2i2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ3422222-2-2-2-200222-22-2-2-22-2-220000000000000000000−2i−2i2i2i−2i−2i2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ3522222-2-2-2-20022-22-22-22-2-22-2000000022-2-222-2-2000000000000i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ3622222-2-2-2-20022-22-22-22-2-22-2000000022-2-222-2-2000000000000−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ3722222-2-2-2-20022-22-22-22-2-22-20000000-2-222-2-222000000000000i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ3822222-2-2-2-20022-22-22-22-2-22-20000000-2-222-2-222000000000000−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ39222-2-222-2-2222-222-2-22-2-2-22222-2-22-2-200000000-2-2220000000022-2-2-2-222000000000000000000000000
χ40222-2-222-2-2222-222-2-22-2-2-22222-2-22-2-200000000-2-22200000000-2-22222-2-2000000000000000000000000
χ41222-2-222-2-222-222-2-22-2-2222-2-2-2-2-222200000000-222-20000000000000000000000002i−2i−2i2i000000000000
χ42222-2-222-2-222-222-2-22-2-2222-2-2-2-2-222200000000-222-2000000000000000000000000−2i2i2i−2i000000000000
χ43222-2-222-2-222-22-222-2-22-22-22-2-2-2-2222000000002-2-220000000000000000000000000000000000002i−2i−2i2i
χ44222-2-222-2-222-22-222-2-22-22-22-2-2-2-2222000000002-2-22000000000000000000000000000000000000−2i2i2i−2i
χ45222-2-222-2-2-2-22-222-2-22-2-2-222-2-222-2220000000022-2-2000000000000000022-2-2-2-2220000000000000000
χ46222-2-222-2-2-2-22-222-2-22-2-2-222-2-222-2220000000022-2-20000000000000000-2-22222-2-20000000000000000
χ47222-2-222-2-2-2-22-2-2-222222-2-2-2-2-222-2222i2i2i2i−2i−2i−2i−2i-2-222−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ48222-2-222-2-2-2-22-2-2-222222-2-2-2-2-222-222−2i−2i−2i−2i2i2i2i2i-2-2222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ49222-2-222-2-2-2-2-222-2-22-2-2222-22222-2-2-2000000002-2-2200000000000000000000000000002-2-2200000000
χ50222-2-222-2-2-2-2-222-2-22-2-2222-22222-2-2-2000000002-2-220000000000000000000000000000-222-200000000
χ51222-2-222-2-2-2-2-22-222-2-22-22-222222-2-2-200000000-222-2000000000000000000000000000000002-2-220000
χ52222-2-222-2-2-2-2-22-222-2-22-22-222222-2-2-200000000-222-200000000000000000000000000000000-222-20000
χ53222-2-2-2-222002-22-2-22-22-22-2200000002i2i−2i−2i−2i−2i2i2i000000000000i2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000000000
χ54222-2-2-2-222002-22-2-22-22-22-2200000002i2i−2i−2i−2i−2i2i2i000000000000−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000000000
χ55222-2-2-2-222002-22-2-22-22-22-220000000−2i−2i2i2i2i2i−2i−2i000000000000i2−i2−i2i2−i2i2i2−i22−2−22−222−20000000000000000
χ56222-2-2-2-222002-22-2-22-22-22-220000000−2i−2i2i2i2i2i−2i−2i000000000000−i2i2i2−i2i2−i2−i2i2−222−22−2−220000000000000000
χ57222-2-2-2-222002-2-222-2-2-2222-2000000000000000000022-2-2-2-222i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ58222-2-2-2-222002-2-222-2-2-2222-2000000000000000000022-2-2-2-222−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ59222-2-2-2-222002-2-222-2-2-2222-20000000000000000000-2-22222-2-2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ60222-2-2-2-222002-2-222-2-2-2222-20000000000000000000-2-22222-2-2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ6144444-4-4-4-400-4-444444-4-44-4-400000000000000000000000000000000000000000000000000000000000
χ6244444-4-4-4-400-4-4-4-4-4-444444400000000000000000000000000000000000000000000000000000000000
χ63444-4-4-4-44400-4444-4-4444-4-4-400000000000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44400-44-4-4444-4-4-44400000000000000000000000000000000000000000000000000000000000
χ6544-44-44-4-44000000000000004i−4i0004i−4i2i−2i2i−2i2i−2i2i−2i00002-22-22-22-200000000000000000000000000000000
χ6644-44-44-4-44000000000000004i−4i0004i−4i−2i2i−2i2i−2i2i−2i2i0000-22-22-22-2200000000000000000000000000000000
χ6744-44-44-4-4400000000000000−4i4i000−4i4i2i−2i2i−2i2i−2i2i−2i0000-22-22-22-2200000000000000000000000000000000
χ6844-44-44-4-4400000000000000−4i4i000−4i4i−2i2i−2i2i−2i2i−2i2i00002-22-22-22-200000000000000000000000000000000
χ6944-44-4-444-444000000000000004-4-4002i−2i−2i2i2i−2i−2i2i00002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ7044-44-4-444-444000000000000004-4-400−2i2i2i−2i−2i2i2i−2i0000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7144-44-4-444-4-4-400000000000000-444002i−2i−2i2i2i−2i−2i2i0000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7244-44-4-444-4-4-400000000000000-44400−2i2i2i−2i−2i2i2i−2i00002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ7344-4-444-44-4000000000000004i−4i000−4i4i2-22-2-22-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ7444-4-444-44-4000000000000004i−4i000−4i4i-22-222-22-200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ7544-4-444-44-400000000000000−4i4i0004i−4i2-22-2-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ7644-4-444-44-400000000000000−4i4i0004i−4i-22-222-22-20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ7744-4-44-44-444400000000000000-44-4002-2-22-222-200002-2-22-222-200000000000000000000000000000000
χ7844-4-44-44-444400000000000000-44-400-222-22-2-220000-222-22-2-2200000000000000000000000000000000
χ7944-4-44-44-44-4-4000000000000004-44002-2-22-222-20000-222-22-2-2200000000000000000000000000000000
χ8044-4-44-44-44-4-4000000000000004-4400-222-22-2-2200002-2-22-222-200000000000000000000000000000000
χ8116-1600000008i2−8i200000000000000000000000000000000000000000000000000000000000000000000000
χ8216-160000000−8i28i200000000000000000000000000000000000000000000000000000000000000000000000

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