Finite Group Databasebeta

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C2×C13×C3⋊D3×C49 #37524315

order22932
automorphism?
homologyAbelianization (H1) = C22×C13×C49 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C13×C3⋊D3×C49
unambiguous semidirect product(C2×C3)⋊(D3×C13×C49)

Splittings

FittingC2×C32×C13×C49 ⋊ C2
derived, SylowC32 ⋊ C22×C13×C49
HallC32×C13×C49 ⋊ C22
HallC32×C49 ⋊ C22×C13
HallC32×C13 ⋊ C22×C49

Subgroups

subgroupG/H
center, hypercenterC2×C13×C49C3⋊D3
commutator, hypocenterC32C22×C13×C49
FrattiniC7C2×C7×C13×C3⋊D3
FittingC2×C32×C13×C49C2
socleC2×C32×C7×C13C2×C7
prime radicalC2×C7×C13×C3⋊D3C7
cosocleC32×C7C22×C7×C13
LCSG ▷ C32
UCSC1 ◁ C2×C13×C49

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11466

Conjugacy classes & character table

7644 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 260);