Finite Group Databasebeta

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C3×C4×C72×C13⋊C3 #37524822

order22932
automorphism?
homologyAbelianization (H1) = C32×C4×C72 · Schur multiplier (H2) = C3×C7

Aliases

direct productC3×C4×C72×C13⋊C3
unambiguous semidirect product(C4×C13)⋊(C32×C72)
unambiguous semidirect product(C3×C4×C13)⋊(C3×C72)

Splittings

FittingC3×C4×C72×C13 ⋊ C3
derived, SylowC13 ⋊ C32×C4×C72
HallC4×C72×C13 ⋊ C32
HallC72×C13 ⋊ C32×C4
HallC4×C13 ⋊ C32×C72

Subgroups

subgroupG/H
center, hypercenterC3×C4×C72C13⋊C3
commutator, hypocenterC13C32×C4×C72
FrattiniC2C2×C3×C72×C13⋊C3
FittingC3×C4×C72×C13C3
socleC2×C3×C72×C13C2×C3
prime radicalC2×C3×C72×C13⋊C3C2
cosocleC2×C13C2×C32×C72
LCSG ▷ C13
UCSC1 ◁ C3×C4×C72

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

4116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 767);