Finite Group Databasebeta

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C3×C11×D7⋊(C52⋊C3) #46831587

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C11×D7⋊(C52⋊C3)
unambiguous semidirect product(C3×D7)⋊(C11×C52⋊C3)
unambiguous semidirect product(C3×C11×D7)⋊(C52⋊C3)

Splittings

Fitting, socleC3×C52×C7×C11 ⋊ C2×C3
derived, HallC52×C7 ⋊ C2×C32×C11
HallC3×C11×C7⋊(C52⋊C3) ⋊ C2
HallC52×C11×D7 ⋊ C32
HallC52×C7×C11 ⋊ C2×C32
HallC3×C7⋊(C52⋊C3) ⋊ C2×C11
HallC52×D7 ⋊ C32×C11
HallC52×C11 ⋊ C3×AGL(1,𝔽7)
HallC11×D7 ⋊ C3×C52⋊C3
HallC7×C11 ⋊ C2×C3×C52⋊C3
SylowC52 ⋊ C3×C11×AGL(1,𝔽7)
HallD7 ⋊ C3×C11×C52⋊C3
SylowC7 ⋊ C2×C3×C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C11D7⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C7C2×C32×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C3×C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

1551 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 230);