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C4×ΓL(1,𝔽8)×C283 #37557766

order23772
automorphism?
homologyAbelianization (H1) = C3×C4×C283 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C283
unambiguous semidirect product(C4×C7)⋊(C3×C283)

Splittings

Fitting, HallC4×C7×C283 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C283
HallC7×C283 ⋊ C3×C4
HallC4×C7 ⋊ C3×C283

Subgroups

subgroupG/H
center, hypercenterC4×C283ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C283
FrattiniC2C2×ΓL(1,𝔽8)×C283
FittingC4×C7×C283C3
socleC2×C7×C283C2×C3
prime radicalC2×ΓL(1,𝔽8)×C283C2
cosocleC2×C7C2×C3×C283
LCSG ▷ C7
UCSC1 ◁ C4×C283

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7924

Conjugacy classes & character table

5660 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23772, 3);