Finite Group Databasebeta

← Group #72299688

Character table — Group #72299688

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1133333333334412121212121212121212121212121212121212121212121212121212121212121212242424242424242424242424242424242424242424242424256256256256256256256256
order122222222222442222222244444444444444444444444444444444444444444444444444336612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ4111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ5111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ6111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ72-222-2-222-2-22-22i−2i000000002i−2i2222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i000000000000000000000000-1-111i−ii−i
χ82-222-2-222-2-22-22i−2i000000002i−2i2222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000001+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7
χ92-222-2-222-2-22-22i−2i000000002i−2i2222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000001−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11
χ102-222-2-222-2-22-2−2i2i00000000−2i2i2222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000-1-111−ii−ii
χ112-222-2-222-2-22-2−2i2i00000000−2i2i2222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000001+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7
χ122-222-2-222-2-22-2−2i2i00000000−2i2i2222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000001−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11
χ13333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1433333333333333-1-1-1-1-1-1-1-13333333333-1-1-1-1-1-1-1-133333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1533333333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-133333333-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1633333333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-13333-1-1-1-100000000
χ1733333333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1333300000000
χ18333333333333-3-311111111-3-33333333311111111-3-3-3-3-3-3-3-3-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-100000000
χ19333333333333-3-311111111-3-3-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-3-3-3-3-1-1-1-1333300000000
χ20333333333333-3-311111111-3-3-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-3-3-3-311113333-1-1-1-100000000
χ21333333333333-3-311111111-3-3-1-1-1-1-1-1-1-1-3-3-3-3-3-3-3-311111111-1-1-1-1333311111111-1-1-1-1-1-1-1-100000000
χ22333333333333-3-3-3-3-3-3-3-3-3-3-3-3-1-1-1-1-1-1-1-111111111111111113333-1-1-1-111111111-1-1-1-1-1-1-1-100000000
χ23333-1-1-1-1-13-1-1-13333-1-1-1-1-1-1-1-111−1+2i−1−2i11−1+2i−1−2i1111−1+2i−1+2i−1−2i−1−2i11−1+2i−1−2i11−1+2i−1−2i3-1-1-111−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i00000000
χ24333-1-1-1-1-13-1-1-13333-1-1-1-1-1-1-1-111−1−2i−1+2i11−1−2i−1+2i1111−1−2i−1−2i−1+2i−1+2i11−1−2i−1+2i11−1−2i−1+2i3-1-1-111−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i00000000
χ25333-1-1-1-1-13-1-1-13333-1-1-1-1-1-1-1-1−1+2i−1−2i11−1+2i−1−2i11−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2i11−1+2i−1−2i113-1-1-1−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i1100000000
χ26333-1-1-1-1-13-1-1-13333-1-1-1-1-1-1-1-1−1−2i−1+2i11−1−2i−1+2i11−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2i11−1−2i−1+2i113-1-1-1−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i1100000000
χ27333-1-1-1-1-13-1-1-133-1-133-1-1-1-1-1-111−1+2i−1−2i11−1+2i−1−2i1111−1−2i−1−2i−1+2i−1+2i11−1+2i−1−2i11−1+2i−1−2i-13-1-111−1−2i−1+2i−1+2i−1−2i11−1−2i−1+2i11−1+2i−1−2i11−1−2i−1+2i1100000000
χ28333-1-1-1-1-13-1-1-133-1-133-1-1-1-1-1-111−1−2i−1+2i11−1−2i−1+2i1111−1+2i−1+2i−1−2i−1−2i11−1−2i−1+2i11−1−2i−1+2i-13-1-111−1+2i−1−2i−1−2i−1+2i11−1+2i−1−2i11−1−2i−1+2i11−1+2i−1−2i1100000000
χ29333-1-1-1-1-13-1-1-133-1-133-1-1-1-1-1-1−1+2i−1−2i11−1+2i−1−2i11−1−2i−1−2i−1+2i−1+2i1111−1+2i−1−2i11−1+2i−1−2i11-13-1-1−1−2i−1+2i1111−1+2i−1−2i11−1−2i−1+2i11−1+2i−1−2i11−1−2i−1+2i00000000
χ30333-1-1-1-1-13-1-1-133-1-133-1-1-1-1-1-1−1−2i−1+2i11−1−2i−1+2i11−1+2i−1+2i−1−2i−1−2i1111−1−2i−1+2i11−1−2i−1+2i11-13-1-1−1+2i−1−2i1111−1−2i−1+2i11−1+2i−1−2i11−1−2i−1+2i11−1+2i−1−2i00000000
χ31333-1-1-1-1-13-1-1-133-1-1-1-133-1-1-1-111−1+2i−1−2i11−1+2i−1−2i−1+2i−1+2i−1−2i−1−2i111111−1+2i−1−2i11−1+2i−1−2i-1-13-1−1+2i−1−2i11−1−2i−1+2i1111−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i00000000
χ32333-1-1-1-1-13-1-1-133-1-1-1-133-1-1-1-111−1−2i−1+2i11−1−2i−1+2i−1−2i−1−2i−1+2i−1+2i111111−1−2i−1+2i11−1−2i−1+2i-1-13-1−1−2i−1+2i11−1+2i−1−2i1111−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i00000000
χ33333-1-1-1-1-13-1-1-133-1-1-1-133-1-1-1-1−1+2i−1−2i11−1+2i−1−2i111111−1+2i−1+2i−1−2i−1−2i−1+2i−1−2i11−1+2i−1−2i11-1-13-111−1+2i−1−2i11−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i−1−2i−1+2i1100000000
χ34333-1-1-1-1-13-1-1-133-1-1-1-133-1-1-1-1−1−2i−1+2i11−1−2i−1+2i111111−1−2i−1−2i−1+2i−1+2i−1−2i−1+2i11−1−2i−1+2i11-1-13-111−1−2i−1+2i11−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i−1+2i−1−2i1100000000
χ35333-1-1-1-1-13-1-1-133-1-1-1-1-1-133-1-111−1+2i−1−2i11−1+2i−1−2i−1−2i−1−2i−1+2i−1+2i111111−1+2i−1−2i11−1+2i−1−2i-1-1-13−1−2i−1+2i1111−1−2i−1+2i−1+2i−1−2i1111−1−2i−1+2i−1+2i−1−2i1100000000
χ36333-1-1-1-1-13-1-1-133-1-1-1-1-1-133-1-111−1−2i−1+2i11−1−2i−1+2i−1+2i−1+2i−1−2i−1−2i111111−1−2i−1+2i11−1−2i−1+2i-1-1-13−1+2i−1−2i1111−1+2i−1−2i−1−2i−1+2i1111−1+2i−1−2i−1−2i−1+2i1100000000
χ37333-1-1-1-1-13-1-1-133-1-1-1-1-1-133-1-1−1+2i−1−2i11−1+2i−1−2i111111−1−2i−1−2i−1+2i−1+2i−1+2i−1−2i11−1+2i−1−2i11-1-1-1311−1−2i−1+2i−1−2i−1+2i1111−1+2i−1−2i−1−2i−1+2i1111−1+2i−1−2i00000000
χ38333-1-1-1-1-13-1-1-133-1-1-1-1-1-133-1-1−1−2i−1+2i11−1−2i−1+2i111111−1+2i−1+2i−1−2i−1−2i−1−2i−1+2i11−1−2i−1+2i11-1-1-1311−1+2i−1−2i−1+2i−1−2i1111−1−2i−1+2i−1+2i−1−2i1111−1−2i−1+2i00000000
χ39333-1-1-1-1-13-1-1-1-3-3111111-3-31111−1+2i−1−2i11−1+2i−1−2i1+2i1+2i1−2i1−2i-1-1-1-1-1-11−2i1+2i-1-11−2i1+2i-1-1-13−1−2i−1+2i11-1-11+2i1−2i1−2i1+2i-1-111−1−2i−1+2i−1+2i−1−2i1100000000
χ40333-1-1-1-1-13-1-1-1-3-3111111-3-31111−1−2i−1+2i11−1−2i−1+2i1−2i1−2i1+2i1+2i-1-1-1-1-1-11+2i1−2i-1-11+2i1−2i-1-1-13−1+2i−1−2i11-1-11−2i1+2i1+2i1−2i-1-111−1+2i−1−2i−1−2i−1+2i1100000000
χ41333-1-1-1-1-13-1-1-1-3-3111111-3-311−1+2i−1−2i11−1+2i−1−2i11-1-1-1-11+2i1+2i1−2i1−2i1−2i1+2i-1-11−2i1+2i-1-1-1-1-1311−1−2i−1+2i1+2i1−2i-1-1-1-11−2i1+2i−1−2i−1+2i1111−1+2i−1−2i00000000
χ42333-1-1-1-1-13-1-1-1-3-3111111-3-311−1−2i−1+2i11−1−2i−1+2i11-1-1-1-11−2i1−2i1+2i1+2i1+2i1−2i-1-11+2i1−2i-1-1-1-1-1311−1+2i−1−2i1−2i1+2i-1-1-1-11+2i1−2i−1+2i−1−2i1111−1−2i−1+2i00000000
χ43333-1-1-1-1-13-1-1-1-3-31111-3-3111111−1+2i−1−2i11−1+2i−1−2i1−2i1−2i1+2i1+2i-1-1-1-1-1-11−2i1+2i-1-11−2i1+2i-1-13-1−1+2i−1−2i111+2i1−2i-1-1-1-11+2i1−2i−1−2i−1+2i1111−1−2i−1+2i00000000
χ44333-1-1-1-1-13-1-1-1-3-31111-3-3111111−1−2i−1+2i11−1−2i−1+2i1+2i1+2i1−2i1−2i-1-1-1-1-1-11+2i1−2i-1-11+2i1−2i-1-13-1−1−2i−1+2i111−2i1+2i-1-1-1-11−2i1+2i−1+2i−1−2i1111−1+2i−1−2i00000000
χ45333-1-1-1-1-13-1-1-1-3-31111-3-31111−1+2i−1−2i11−1+2i−1−2i11-1-1-1-11−2i1−2i1+2i1+2i1−2i1+2i-1-11−2i1+2i-1-1-1-13-111−1+2i−1−2i-1-11+2i1−2i1+2i1−2i-1-111−1−2i−1+2i−1−2i−1+2i1100000000
χ46333-1-1-1-1-13-1-1-1-3-31111-3-31111−1−2i−1+2i11−1−2i−1+2i11-1-1-1-11+2i1+2i1−2i1−2i1+2i1−2i-1-11+2i1−2i-1-1-1-13-111−1−2i−1+2i-1-11−2i1+2i1−2i1+2i-1-111−1+2i−1−2i−1+2i−1−2i1100000000
χ47333-1-1-1-1-13-1-1-1-3-311-3-311111111−1+2i−1−2i11−1+2i−1−2i-1-1-1-11+2i1+2i1−2i1−2i-1-11−2i1+2i-1-11−2i1+2i-13-1-111−1−2i−1+2i1−2i1+2i-1-11+2i1−2i-1-1−1+2i−1−2i11−1−2i−1+2i1100000000
χ48333-1-1-1-1-13-1-1-1-3-311-3-311111111−1−2i−1+2i11−1−2i−1+2i-1-1-1-11−2i1−2i1+2i1+2i-1-11+2i1−2i-1-11+2i1−2i-13-1-111−1+2i−1−2i1+2i1−2i-1-11−2i1+2i-1-1−1−2i−1+2i11−1+2i−1−2i1100000000
χ49333-1-1-1-1-13-1-1-1-3-311-3-3111111−1+2i−1−2i11−1+2i−1−2i111+2i1+2i1−2i1−2i-1-1-1-11−2i1+2i-1-11−2i1+2i-1-1-13-1-1−1−2i−1+2i11-1-11−2i1+2i-1-11+2i1−2i11−1+2i−1−2i11−1−2i−1+2i00000000
χ50333-1-1-1-1-13-1-1-1-3-311-3-3111111−1−2i−1+2i11−1−2i−1+2i111−2i1−2i1+2i1+2i-1-1-1-11+2i1−2i-1-11+2i1−2i-1-1-13-1-1−1+2i−1−2i11-1-11+2i1−2i-1-11−2i1+2i11−1−2i−1+2i11−1+2i−1−2i00000000
χ51333-1-1-1-1-13-1-1-1-3-3-3-31111111111−1+2i−1−2i11−1+2i−1−2i-1-1-1-11−2i1−2i1+2i1+2i-1-11−2i1+2i-1-11−2i1+2i3-1-1-111−1+2i−1−2i-1-11−2i1+2i-1-11−2i1+2i11−1+2i−1−2i11−1+2i−1−2i00000000
χ52333-1-1-1-1-13-1-1-1-3-3-3-31111111111−1−2i−1+2i11−1−2i−1+2i-1-1-1-11+2i1+2i1−2i1−2i-1-11+2i1−2i-1-11+2i1−2i3-1-1-111−1−2i−1+2i-1-11+2i1−2i-1-11+2i1−2i11−1−2i−1+2i11−1−2i−1+2i00000000
χ53333-1-1-1-1-13-1-1-1-3-3-3-311111111−1+2i−1−2i11−1+2i−1−2i111−2i1−2i1+2i1+2i-1-1-1-11−2i1+2i-1-11−2i1+2i-1-13-1-1-1−1+2i−1−2i111−2i1+2i-1-11−2i1+2i-1-1−1+2i−1−2i11−1+2i−1−2i1100000000
χ54333-1-1-1-1-13-1-1-1-3-3-3-311111111−1−2i−1+2i11−1−2i−1+2i111+2i1+2i1−2i1−2i-1-1-1-11+2i1−2i-1-11+2i1−2i-1-13-1-1-1−1−2i−1+2i111+2i1−2i-1-11+2i1−2i-1-1−1−2i−1+2i11−1−2i−1+2i1100000000
χ556-666-6-666-6-66-66i−6i000000006i−6i-2-2-2-2222200000000−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ566-666-6-666-6-66-6−6i6i00000000−6i6i-2-2-2-22222000000002i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ576-66-222-2-2-62-226i−6i00000000−2i2i22−2+4i−2−4i-2-22−4i2+4i000000002i2i−4−2i4−2i−2i−2i4+2i−4+2i00000000000000000000000000000000
χ586-66-222-2-2-62-226i−6i00000000−2i2i22−2−4i−2+4i-2-22+4i2−4i000000002i2i4−2i−4−2i−2i−2i−4+2i4+2i00000000000000000000000000000000
χ596-66-222-2-2-62-226i−6i00000000−2i2i−2+4i−2−4i222−4i2+4i-2-200000000−4−2i4−2i2i2i4+2i−4+2i−2i−2i00000000000000000000000000000000
χ606-66-222-2-2-62-226i−6i00000000−2i2i−2−4i−2+4i222+4i2−4i-2-2000000004−2i−4−2i2i2i−4+2i4+2i−2i−2i00000000000000000000000000000000
χ616-66-222-2-2-62-22−6i6i000000002i−2i22−2+4i−2−4i-2-22−4i2+4i00000000−2i−2i4+2i−4+2i2i2i−4−2i4−2i00000000000000000000000000000000
χ626-66-222-2-2-62-22−6i6i000000002i−2i22−2−4i−2+4i-2-22+4i2−4i00000000−2i−2i−4+2i4+2i2i2i4−2i−4−2i00000000000000000000000000000000
χ636-66-222-2-2-62-22−6i6i000000002i−2i−2+4i−2−4i222−4i2+4i-2-2000000004+2i−4+2i−2i−2i−4−2i4−2i2i2i00000000000000000000000000000000
χ646-66-222-2-2-62-22−6i6i000000002i−2i−2−4i−2+4i222+4i2−4i-2-200000000−4+2i4+2i−2i−2i4−2i−4−2i2i2i00000000000000000000000000000000
χ651212-412-4-4-4-4-4-4-412000000000000000000004-44-44-44-40000000000000000000000000000000000000000
χ661212-412-4-4-4-4-4-4-41200000000000000000000-44-44-44-440000000000000000000000000000000000000000
χ671212-4-412-412-4-4-4-4-4000000000000000000004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000
χ681212-4-412-412-4-4-4-4-400000000000000000000−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000
χ691212-4-4-412-412-4-4-4-4000000000000000000004i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000
χ701212-4-4-412-412-4-4-4-400000000000000000000−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000
χ711212-4-4-4-4-4-4-41212-4000000000000000000004-44-4-44-440000000000000000000000000000000000000000
χ721212-4-4-4-4-4-4-41212-400000000000000000000-44-444-44-40000000000000000000000000000000000000000
χ7312-12-41244-4-444-4-12004-44-44-44-40000000000000000000000000000000000000000000000000000000000
χ7412-12-41244-4-444-4-1200-44-44-44-440000000000000000000000000000000000000000000000000000000000
χ7512-12-4-444-4-44-12124004-44-4-44-440000000000000000000000000000000000000000000000000000000000
χ7612-12-4-444-4-44-1212400-44-444-44-40000000000000000000000000000000000000000000000000000000000
χ7712-12-4-44-12-41244-44004-4-44-444-40000000000000000000000000000000000000000000000000000000000
χ7812-12-4-44-12-41244-4400-444-44-4-440000000000000000000000000000000000000000000000000000000000
χ7912-12-4-4-12412-444-44004-4-444-4-440000000000000000000000000000000000000000000000000000000000
χ8012-12-4-4-12412-444-4400-444-4-444-40000000000000000000000000000000000000000000000000000000000

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