Finite Group Databasebeta

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C13×C22⋊#10620252 #46799610

order33852
automorphism?
homologyAbelianization (H1) = C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×C22⋊#10620252
unambiguous semidirect productC22⋊(C13×#10620252)

Splittings

Fitting, socle, HallC22×C7×C13×C31 ⋊ C3
derived, HallC22×C7×C31 ⋊ C3×C13
HallC7×C13×C31 ⋊ A4
HallC22×C13×C31 ⋊ ΓL(1,𝔽8)
HallC13×C31 ⋊ C22⋊ΓL(1,𝔽8)
HallC22×C7×C13 ⋊ C31⋊C3
HallC7×C31 ⋊ A4×C13
HallC22×C31 ⋊ C13×ΓL(1,𝔽8)
HallC7×C13 ⋊ C22⋊(C31⋊C3)
HallC22×C13 ⋊ #10620252
SylowC31 ⋊ C13×C22⋊ΓL(1,𝔽8)
HallC22×C7 ⋊ C13×C31⋊C3
SylowC7 ⋊ C13×C22⋊(C31⋊C3)
SylowC22 ⋊ C13×#10620252

Subgroups

subgroupG/H
center, hypercenterC13C22⋊#10620252
commutator, cosocle, hypocenterC22×C7×C31C3×C13
FrattiniC1G
Fitting, socleC22×C7×C13×C31C3
LCSG ▷ C22×C7×C31
UCSC1 ◁ C13

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

3796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 405);