Finite Group Databasebeta

← Group #1016

Character table — Group #1016

Order 96.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222211112222221111222222111122222211112222221111222222
order12442224443612126661212123612126661212122244222444661212666121212661212666121212
χ1111111111111111111111111111111111111111111111111111111111111
χ211111-1-11-1-111111-1-11-1-111111-1-11-1-111111-1-11-1-111111-1-11-1-111111-1-11-1-1
χ31111-11-1-11-11111-11-1-11-11111-11-1-11-11111-11-1-11-11111-11-1-11-11111-11-1-11-1
χ41111-1-11-1-111111-1-11-1-111111-1-11-1-111111-1-11-1-111111-1-11-1-111111-1-11-1-11
χ511-1-111-1-1-1111-1-111-1-1-1111-1-111-1-1-1111-1-111-1-1-1111-1-111-1-1-1111-1-111-1-1-11
χ611-1-11-11-11-111-1-11-11-11-111-1-11-11-11-111-1-11-11-11-111-1-11-11-11-111-1-11-11-11-1
χ711-1-1-1111-1-111-1-1-1111-1-111-1-1-1111-1-111-1-1-1111-1-111-1-1-1111-1-111-1-1-1111-1-1
χ811-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-1111
χ92-22i−2i0000002-22i−2i0000002-22i−2i0000002-22i−2i0000002-22i−2i0000002-22i−2i000000
χ102-2−2i2i0000002-2−2i2i0000002-2−2i2i0000002-2−2i2i0000002-2−2i2i0000002-2−2i2i000000
χ111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ1211111-1-11-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i3211111-1-11-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32
χ131111-11-1-11-1−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i321111-11-1-11-1−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32
χ141111-1-11-1-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321111-1-11-1-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32
χ1511-1-111-1-1-11−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i3211-1-111-1-1-11−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32
χ1611-1-11-11-11-1−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i3211-1-11-11-11-1−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32
χ1711-1-1-1111-1-1−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i3211-1-1-1111-1-1−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32
χ1811-1-1-1-1-1111−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i3211-1-1-1-1-1111−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32
χ192-22i−2i000000−1+i31−i32ζ7−2ζ7000000−1−i31+i32ζ11−2ζ110000002-22i−2i000000−1+i31−i32ζ7−2ζ7000000−1−i31+i32ζ11−2ζ11000000
χ202-2−2i2i000000−1+i31−i3−2ζ72ζ7000000−1−i31+i3−2ζ112ζ110000002-2−2i2i000000−1+i31−i3−2ζ72ζ7000000−1−i31+i3−2ζ112ζ11000000
χ211111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ2211111-1-11-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i3211111-1-11-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32
χ231111-11-1-11-1−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i321111-11-1-11-1−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32
χ241111-1-11-1-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321111-1-11-1-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32
χ2511-1-111-1-1-11−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i3211-1-111-1-1-11−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32
χ2611-1-11-11-11-1−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i3211-1-11-11-11-1−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32
χ2711-1-1-1111-1-1−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i3211-1-1-1111-1-1−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32
χ2811-1-1-1-1-1111−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i3211-1-1-1-1-1111−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32
χ292-22i−2i000000−1−i31+i32ζ11−2ζ11000000−1+i31−i32ζ7−2ζ70000002-22i−2i000000−1−i31+i32ζ11−2ζ11000000−1+i31−i32ζ7−2ζ7000000
χ302-2−2i2i000000−1−i31+i3−2ζ112ζ11000000−1+i31−i3−2ζ72ζ70000002-2−2i2i000000−1−i31+i3−2ζ112ζ11000000−1+i31−i3−2ζ72ζ7000000
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3211111-1-11-1-111111-1-11-1-111111-1-11-1-1-1-1-1-1-111-111-1-1-1-1-111-111-1-1-1-1-111-111
χ331111-11-1-11-11111-11-1-11-11111-11-1-11-1-1-1-1-11-111-11-1-1-1-11-111-11-1-1-1-11-111-11
χ341111-1-11-1-111111-1-11-1-111111-1-11-1-11-1-1-1-111-111-1-1-1-1-111-111-1-1-1-1-111-111-1
χ3511-1-111-1-1-1111-1-111-1-1-1111-1-111-1-1-11-1-111-1-1111-1-1-111-1-1111-1-1-111-1-1111-1
χ3611-1-11-11-11-111-1-11-11-11-111-1-11-11-11-1-1-111-11-11-11-1-111-11-11-11-1-111-11-11-11
χ3711-1-1-1111-1-111-1-1-1111-1-111-1-1-1111-1-1-1-1111-1-1-111-1-1111-1-1-111-1-1111-1-1-111
χ3811-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-1111-1-111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1
χ392-22i−2i0000002-22i−2i0000002-22i−2i000000-22−2i2i000000-22−2i2i000000-22−2i2i000000
χ402-2−2i2i0000002-2−2i2i0000002-2−2i2i000000-222i−2i000000-222i−2i000000-222i−2i000000
χ411111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32
χ4211111-1-11-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32-1-1-1-1-111-1111−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32
χ431111-11-1-11-1−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32-1-1-1-11-111-111−i321−i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i32
χ441111-1-11-1-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32-1-1-1-111-111-11−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ4511-1-111-1-1-11−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32-1-111-1-1111-11−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32
χ4611-1-11-11-11-1−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32-1-111-11-11-111−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32
χ4711-1-1-1111-1-1−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32-1-1111-1-1-1111−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32
χ4811-1-1-1-1-1111−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32-1-111111-1-1-11−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32
χ492-22i−2i000000−1+i31−i32ζ7−2ζ7000000−1−i31+i32ζ11−2ζ11000000-22−2i2i0000001−i3−1+i3−2ζ72ζ70000001+i3−1−i3−2ζ112ζ11000000
χ502-2−2i2i000000−1+i31−i3−2ζ72ζ7000000−1−i31+i3−2ζ112ζ11000000-222i−2i0000001−i3−1+i32ζ7−2ζ70000001+i3−1−i32ζ11−2ζ11000000
χ511111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32
χ5211111-1-11-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32-1-1-1-1-111-1111+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32
χ531111-11-1-11-1−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32-1-1-1-11-111-111+i321+i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i32
χ541111-1-11-1-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32-1-1-1-111-111-11+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ5511-1-111-1-1-11−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32-1-111-1-1111-11+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32
χ5611-1-11-11-11-1−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32-1-111-11-11-111+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32
χ5711-1-1-1111-1-1−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32-1-1111-1-1-1111+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32
χ5811-1-1-1-1-1111−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32-1-111111-1-1-11+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32
χ592-22i−2i000000−1−i31+i32ζ11−2ζ11000000−1+i31−i32ζ7−2ζ7000000-22−2i2i0000001+i3−1−i3−2ζ112ζ110000001−i3−1+i3−2ζ72ζ7000000
χ602-2−2i2i000000−1−i31+i3−2ζ112ζ11000000−1+i31−i3−2ζ72ζ7000000-222i−2i0000001+i3−1−i32ζ11−2ζ110000001−i3−1+i32ζ7−2ζ7000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.