Finite Group Databasebeta

← Prev (#37555527) Next (#37555529) →

C4×C13⋊C3×C151 #37555528

order23556
automorphism?
homologyAbelianization (H1) = C3×C4×C151 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13⋊C3×C151
unambiguous semidirect product(C4×C13)⋊(C3×C151)

Splittings

Fitting, HallC4×C13×C151 ⋊ C3
derived, SylowC13 ⋊ C3×C4×C151
HallC13×C151 ⋊ C3×C4
HallC4×C13 ⋊ C3×C151

Subgroups

subgroupG/H
center, hypercenterC4×C151C13⋊C3
commutator, hypocenterC13C3×C4×C151
FrattiniC2C2×C13⋊C3×C151
FittingC4×C13×C151C3
socleC2×C13×C151C2×C3
prime radicalC2×C13⋊C3×C151C2
cosocleC2×C13C2×C3×C151
LCSG ▷ C13
UCSC1 ◁ C4×C151

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7852

Conjugacy classes & character table

4228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23556, 3);