Finite Group Databasebeta

C4×#15689809 #26376172

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#15689809

Splittings

FittingC4×#126×C47 ⋊ C2
SylowC47 ⋊ C4×#552

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC4×#126×C47C2
socle, cosocleC23×C47C25
prime radicalC22×C22⋊D47C23
hypercenterC4×#126D47
hypocenterC47C4×#552
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#126

2376 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 329462);