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C4×ΓL(1,𝔽8)×C37⋊C3 #22605148

order9324
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC4×ΓL(1,𝔽8)×C37⋊C3
unambiguous semidirect product(C4×C7×C37⋊C3)⋊C3
unambiguous semidirect product(C4×ΓL(1,𝔽8)×C37)⋊C3
unambiguous semidirect product(C4×#11715913)⋊C3
unambiguous semidirect product(C4×#11715912)⋊C3

Splittings

Fitting, HallC4×C7×C37 ⋊ C32
derived, HallC7×C37 ⋊ C32×C4
HallC4×C37 ⋊ C3×ΓL(1,𝔽8)
SylowC37 ⋊ C3×C4×ΓL(1,𝔽8)
HallC4×C7 ⋊ C3×C37⋊C3
SylowC7 ⋊ C3×C4×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC4ΓL(1,𝔽8)×C37⋊C3
commutator, hypocenterC7×C37C32×C4
FrattiniC2C2×ΓL(1,𝔽8)×C37⋊C3
FittingC4×C7×C37C32
socleC2×C7×C37C2×C32
LCSG ▷ C7×C37
UCSC1 ◁ C4

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

300 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9324, 93);