Finite Group Databasebeta

← Prev (#37524688) Next (#37524690) →

C4×C13×ΓL(1,𝔽8)2 #37524689

order22932
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC4×C13×ΓL(1,𝔽8)2
unambiguous semidirect product(C4×C7×ΓL(1,𝔽8))⋊(C3×C13)
unambiguous semidirect product(C4×#3861)⋊(C3×C13)
unambiguous semidirect product(C4×#3862)⋊(C3×C13)

Splittings

Fitting, HallC4×C72×C13 ⋊ C32
derived, SylowC72 ⋊ C32×C4×C13
HallC72×C13 ⋊ C32×C4
HallC4×C72 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC4×C13ΓL(1,𝔽8)2
commutator, hypocenterC72C32×C4×C13
FrattiniC2C2×C13×ΓL(1,𝔽8)2
FittingC4×C72×C13C32
socleC2×C72×C13C2×C32
prime radicalC2×C13×ΓL(1,𝔽8)2C2
cosocleC2×C72C2×C32×C13
LCSG ▷ C72
UCSC1 ◁ C4×C13

168 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1092

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 634);