Finite Group Databasebeta

C22×C4×(C2×D47)⋊C4 #26374452

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×C4×(C2×D47)⋊C4

Splittings

FittingC23×C42×C47 ⋊ C2
SylowC47 ⋊ C22×C4×C22⋊C4

Subgroups

subgroupG/H
centerC24×C4C2×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC23×C42×C47C2
socleC25×C47C23
prime radicalC25×D47C22
cosocleC23×C47C25
hypercenterC23×C42D47
hypocenterC47C22×C4×C22⋊C4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C24×C4 ◁ C23×C42

9534 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327742);