Finite Group Databasebeta

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C13×C3⋊((C49⋊C3)⋊C4) #37524159

order22932
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊((C49⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C13×(C49⋊C3)⋊C4)
unambiguous semidirect product(C49⋊C3)⋊(Dic3×C13)
unambiguous semidirect productDic147⋊(C3×C13)

Splittings

derivedC3×C49 ⋊ C3×C4×C13
HallC3×C13×C49⋊C3 ⋊ C4
HallC13×C49 ⋊ C3×Dic3
HallC3×C49⋊C3 ⋊ C4×C13
SylowC49 ⋊ C3×Dic3×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊(D49⋊C3)
commutator, hypocenterC3×C49C3×C4×C13
FrattiniC2×C7C13×C3⋊AGL(1,𝔽7)
FittingC2×C3×C13×C49C2×C3
socleC2×C3×C7×C13AGL(1,𝔽7)
prime radicalC2×C3×C13×C49⋊C3C2
cosocleC2×C3×C49C2×C3×C13
LCSG ▷ C3×C49
UCSC1 ◁ C2×C13

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 104);