Finite Group Databasebeta

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C49×C3⋊(Dic13⋊C3) #37524150

order22932
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×C3⋊(Dic13⋊C3)
unambiguous semidirect productC3⋊(C49×Dic13⋊C3)
unambiguous semidirect productDic39⋊(C3×C49)

Splittings

derivedC3×C13 ⋊ C3×C4×C49
HallC3×C13⋊C3×C49 ⋊ C4
HallC13×C49 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C49
SylowC13 ⋊ C3×Dic3×C49

Subgroups

subgroupG/H
center, hypercenterC2×C49C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C49
FrattiniC2×C7C7×C3⋊(D13⋊C3)
FittingC2×C3×C13×C49C2×C3
socle, cosocleC2×C3×C7×C13C2×C3×C7
prime radicalC2×C3×C7×C13⋊C3C2×C7
LCSG ▷ C3×C13
UCSC1 ◁ C2×C49

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 95);