Finite Group Databasebeta

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C3×C4×C13×C49⋊C3 #37524166

order22932
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C13×C49⋊C3
unambiguous semidirect product(C4×C49)⋊(C32×C13)
unambiguous semidirect product(C3×C4×C49)⋊(C3×C13)

Splittings

FittingC3×C4×C13×C49 ⋊ C3
derived, SylowC49 ⋊ C32×C4×C13
HallC4×C13×C49 ⋊ C32
HallC13×C49 ⋊ C32×C4
HallC4×C49 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC3×C4×C13C49⋊C3
commutator, hypocenterC49C32×C4×C13
FrattiniC2×C7C2×C3×C13×ΓL(1,𝔽8)
FittingC3×C4×C13×C49C3
socleC2×C3×C7×C13C2×ΓL(1,𝔽8)
prime radicalC2×C3×C13×C49⋊C3C2
cosocleC2×C49C2×C32×C13
LCSG ▷ C49
UCSC1 ◁ C3×C4×C13

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

2964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 111);