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C4×C7×ΓL(1,𝔽8)×C13⋊C3 #37524686

order22932
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC4×C7×ΓL(1,𝔽8)×C13⋊C3
unambiguous semidirect product(C4×C7×C13⋊C3)⋊(C3×C7)
unambiguous semidirect product(C4×C13×ΓL(1,𝔽8))⋊(C3×C7)
unambiguous semidirect product(C4×#63270)⋊(C3×C7)
unambiguous semidirect product(C4×#63271)⋊(C3×C7)

Splittings

Fitting, HallC4×C72×C13 ⋊ C32
derivedC7×C13 ⋊ C32×C4×C7
HallC72×C13 ⋊ C32×C4
HallC4×C72 ⋊ C3×C13⋊C3
HallC4×C13 ⋊ C3×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×C4×C13⋊C3
SylowC13 ⋊ C3×C4×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC4×C7ΓL(1,𝔽8)×C13⋊C3
commutator, hypocenterC7×C13C32×C4×C7
FrattiniC2C2×C7×ΓL(1,𝔽8)×C13⋊C3
FittingC4×C72×C13C32
socleC2×C72×C13C2×C32
prime radicalC2×C7×ΓL(1,𝔽8)×C13⋊C3C2
cosocleC2×C7×C13C2×C32×C7
LCSG ▷ C7×C13
UCSC1 ◁ C4×C7

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 631);