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C13×C31×C22⋊ΓL(1,𝔽8) #46799609

order33852
automorphism?
homologyAbelianization (H1) = C3×C13×C31 · Schur multiplier (H2) = C2

Aliases

direct productC13×C31×C22⋊ΓL(1,𝔽8)
unambiguous semidirect productC22⋊(C13×ΓL(1,𝔽8)×C31)
unambiguous semidirect productC7⋊(A4×C13×C31)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC13×C31C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C3×C13×C31
FrattiniC1G
Fitting, socleC22×C7×C13×C31C3
LCSG ▷ C22×C7
UCSC1 ◁ C13×C31

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

4836 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 404);