Finite Group Databasebeta

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C4×C13⋊C3×C157 #37587553

order24492
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C157 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13⋊C3×C157
unambiguous semidirect product(C4×C13)⋊(C3×C157)

Splittings

Fitting, HallC4×C13×C157 ⋊ C3
derived, SylowC13 ⋊ C3×C4×C157
HallC13×C157 ⋊ C3×C4
HallC4×C13 ⋊ C3×C157

Subgroups

subgroupG/H
center, hypercenterC4×C157C13⋊C3
commutator, hypocenterC13C3×C4×C157
FrattiniC2C2×C13⋊C3×C157
FittingC4×C13×C157C3
socleC2×C13×C157C2×C3
prime radicalC2×C13⋊C3×C157C2
cosocleC2×C13C2×C3×C157
LCSG ▷ C13
UCSC1 ◁ C4×C157

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24492, 4);