Finite Group Databasebeta

C4×#15689132 #26214062

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#15689132

Splittings

SylowC47 ⋊ C4×#419

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC22×C4×Q8×C47C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC22×C4×Q8D47
hypocenterC47C4×#419
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×Q8

1586 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167352);