Finite Group Databasebeta

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ΓL(1,𝔽8)2×C53 #37552615

order23373
automorphism?
homologyAbelianization (H1) = C32×C53 · Schur multiplier (H2) = C3

Aliases

direct productΓL(1,𝔽8)2×C53
unambiguous semidirect product(C7×ΓL(1,𝔽8))⋊(C3×C53)
unambiguous semidirect product#3861⋊(C3×C53)
unambiguous semidirect product#3862⋊(C3×C53)
unambiguous semidirect product(C53×#3862)⋊C3
unambiguous semidirect product(C7×ΓL(1,𝔽8)×C53)⋊C3
unambiguous semidirect product(C53×#3861)⋊C3

Splittings

Fitting, socle, HallC72×C53 ⋊ C32
derived, SylowC72 ⋊ C32×C53

Subgroups

subgroupG/H
center, hypercenterC53ΓL(1,𝔽8)2
commutator, cosocle, hypocenterC72C32×C53
FrattiniC1G
Fitting, socleC72×C53C32
LCSG ▷ C72
UCSC1 ◁ C53

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1113

Conjugacy classes & character table

1325 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23373, 10);