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C7×C13⋊C3×C22⋊ΓL(1,𝔽8) #37525387

order22932
automorphism?
homologyAbelianization (H1) = C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC7×C13⋊C3×C22⋊ΓL(1,𝔽8)
unambiguous semidirect product(C22×C13⋊C3)⋊(C7×ΓL(1,𝔽8))
unambiguous semidirect product(C7×C13⋊C3)⋊(C7×A4)

Splittings

Fitting, socle, HallC22×C72×C13 ⋊ C32
derivedC22×C7×C13 ⋊ C32×C7
HallC72×C13 ⋊ C3×A4
HallC22×C72 ⋊ C3×C13⋊C3
HallC22×C13 ⋊ C3×C7×ΓL(1,𝔽8)
SylowC72 ⋊ A4×C13⋊C3
SylowC13 ⋊ C3×C7×C22⋊ΓL(1,𝔽8)
SylowC22 ⋊ C7×ΓL(1,𝔽8)×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C13⋊C3×C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7×C13C32×C7
FrattiniC1G
Fitting, socleC22×C72×C13C32
LCSG ▷ C22×C7×C13
UCSC1 ◁ C7

152 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 34 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) = 546

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1332);