Finite Group Databasebeta

C4×#15689600 #26374526

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#15689600

Splittings

SylowC47 ⋊ C4×#519

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC4×#117×C47C2
socle, cosocleC23×C47C25
prime radicalC24×C47C24
hypercenterC4×#117D47
hypocenterC47C4×#519
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#117

3402 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327816);