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ΓL(1,𝔽8)×C373⋊C3 #37555054

order23499
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

direct productΓL(1,𝔽8)×C373⋊C3
unambiguous semidirect product(ΓL(1,𝔽8)×C373)⋊C3
unambiguous semidirect product(C7×C373⋊C3)⋊C3
unambiguous semidirect product#21463179⋊C3
unambiguous semidirect product#21463180⋊C3

Splittings

Fitting, socle, derived, HallC7×C373 ⋊ C32
SylowC373 ⋊ C3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C373⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C373C32
LCSG ▷ C7×C373
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2611

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23499, 7);