Finite Group Databasebeta

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C7×ΓL(1,𝔽8)×AGL(1,𝔽13) #37524876

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

Aliases

direct productC7×ΓL(1,𝔽8)×AGL(1,𝔽13)
unambiguous semidirect product(C7×AGL(1,𝔽13))⋊(C3×C7)
unambiguous semidirect product(ΓL(1,𝔽8)×#261)⋊(C3×C7)
unambiguous semidirect product#11763981⋊(C3×C7)
unambiguous semidirect product#11763982⋊(C3×C7)

Splittings

Fitting, socle, HallC72×C13 ⋊ C32×C4
derivedC7×C13 ⋊ C32×C4×C7
HallC7×ΓL(1,𝔽8)×C13⋊C3 ⋊ C4
HallC72×#261 ⋊ C32
Hall#261 ⋊ C3×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×AGL(1,𝔽13)
SylowC13 ⋊ C3×C4×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC7ΓL(1,𝔽8)×AGL(1,𝔽13)
commutator, hypocenterC7×C13C32×C4×C7
FrattiniC1G
Fitting, socleC72×C13C32×C4
prime radicalC7×ΓL(1,𝔽8)×D13⋊C3C2
cosocleC7×D13C2×C32×C7
LCSG ▷ C7×C13
UCSC1 ◁ C7

168 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 273

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 821);