Finite Group Databasebeta

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C3×D11×C7⋊(C52⋊C3) #46831589

order34650
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×D11×C7⋊(C52⋊C3)
unambiguous semidirect productC11⋊(C2×C3×C7⋊(C52⋊C3))
unambiguous semidirect product(C3×C7×D11)⋊(C52⋊C3)
unambiguous semidirect product(C3×C52×D11)⋊ΓL(1,𝔽8)

Splittings

Fitting, socleC3×C52×C7×C11 ⋊ C2×C3
derived, HallC52×C7×C11 ⋊ C2×C32
HallC3×C11×C7⋊(C52⋊C3) ⋊ C2
HallC52×C7×D11 ⋊ C32
HallC52×D11 ⋊ C3×ΓL(1,𝔽8)
HallC52×C11 ⋊ C2×C3×ΓL(1,𝔽8)
HallC52×C7 ⋊ C32×D11
HallC7×D11 ⋊ C3×C52⋊C3
HallC7×C11 ⋊ C2×C3×C52⋊C3
SylowC52 ⋊ C3×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×C3×C7⋊(C52⋊C3)
SylowC7 ⋊ C3×D11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC3D11×C7⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C7×C11C2×C32
FrattiniC1G
Fitting, socleC3×C52×C7×C11C2×C3
LCSG ▷ C52×C7×C11
UCSC1 ◁ C3

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

1281 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 232);