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C4×ΓL(1,𝔽8)×C281 #37556226

order23604
automorphism?
homologyAbelianization (H1) = C3×C4×C281 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C281
unambiguous semidirect product(C4×C7)⋊(C3×C281)
unambiguous semidirect product(C4×C7×C281)⋊C3

Splittings

Fitting, HallC4×C7×C281 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C281
HallC7×C281 ⋊ C3×C4
HallC4×C7 ⋊ C3×C281

Subgroups

subgroupG/H
center, hypercenterC4×C281ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C281
FrattiniC2C2×ΓL(1,𝔽8)×C281
FittingC4×C7×C281C3
socleC2×C7×C281C2×C3
prime radicalC2×ΓL(1,𝔽8)×C281C2
cosocleC2×C7C2×C3×C281
LCSG ▷ C7
UCSC1 ◁ C4×C281

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7868

Conjugacy classes & character table

5620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23604, 3);