Finite Group Databasebeta

← Prev (#46799210) Next (#46799212) →

C4×C13×ΓL(1,𝔽8)×C31 #46799211

order33852
automorphism?
homologyAbelianization (H1) = C3×C4×C13×C31 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×ΓL(1,𝔽8)×C31
unambiguous semidirect product(C4×C7)⋊(C3×C13×C31)

Splittings

Fitting, HallC4×C7×C13×C31 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C13×C31
HallC7×C13×C31 ⋊ C3×C4
HallC4×C7×C31 ⋊ C3×C13
HallC4×C7×C13 ⋊ C3×C31
HallC7×C31 ⋊ C3×C4×C13
HallC7×C13 ⋊ C3×C4×C31
HallC4×C7 ⋊ C3×C13×C31

Subgroups

subgroupG/H
center, hypercenterC4×C13×C31ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C13×C31
FrattiniC2C2×C13×ΓL(1,𝔽8)×C31
FittingC4×C7×C13×C31C3
socleC2×C7×C13×C31C2×C3
prime radicalC2×C13×ΓL(1,𝔽8)×C31C2
cosocleC2×C7C2×C3×C13×C31
LCSG ▷ C7
UCSC1 ◁ C4×C13×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

8060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 6);