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C3×ΓL(1,𝔽8)×C71⋊C5 #36375362

order22365
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×C71⋊C5
unambiguous semidirect productC7⋊(C32×C71⋊C5)
unambiguous semidirect product(C3×C7)⋊(C3×C71⋊C5)
unambiguous semidirect productC71⋊(C3×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C71)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×C71)⋊(C3×C5)
unambiguous semidirect product(C7×C71⋊C5)⋊C32
unambiguous semidirect product(C3×ΓL(1,𝔽8)×C71)⋊C5
unambiguous semidirect product(C3×C7×C71⋊C5)⋊C3

Splittings

Fitting, socleC3×C7×C71 ⋊ C3×C5
derived, HallC7×C71 ⋊ C32×C5
HallC3×ΓL(1,𝔽8)×C71 ⋊ C5
HallC7×C71⋊C5 ⋊ C32
SylowC71 ⋊ C3×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C32×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×C71⋊C5
commutator, cosocle, hypocenterC7×C71C32×C5
FrattiniC1G
Fitting, socleC3×C7×C71C3×C5
LCSG ▷ C7×C71
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1491

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22365, 9);