Finite Group Databasebeta

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D11×C7⋊(C52⋊C9) #46831504

order34650
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C5

Aliases

direct productD11×C7⋊(C52⋊C9)
unambiguous semidirect productC11⋊(C2×C7⋊(C52⋊C9))
unambiguous semidirect product(C7×D11)⋊(C52⋊C9)
unambiguous semidirect product(C52×D11)⋊(C7⋊C9)

Splittings

derived, HallC52×C7×C11 ⋊ C2×C9
HallC11×C7⋊(C52⋊C9) ⋊ C2
HallC52×C7×D11 ⋊ C9
HallC52×D11 ⋊ C7⋊C9
HallC52×C11 ⋊ C2×C7⋊C9
HallC52×C7 ⋊ C9×D11
HallC7×D11 ⋊ C52⋊C9
HallC7×C11 ⋊ C2×C52⋊C9
SylowC52 ⋊ D11×C7⋊C9
SylowC11 ⋊ C2×C7⋊(C52⋊C9)
SylowC7 ⋊ D11×C52⋊C9

Subgroups

subgroupG/H
center, Frattini, hypercenterC3D11×C7⋊(C52⋊C3)
commutator, hypocenterC52×C7×C11C2×C9
Fitting, socle, cosocleC3×C52×C7×C11C2×C3
prime radicalC3×C52×C7×D11C3
LCSG ▷ C52×C7×C11
UCSC1 ◁ C3

80 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, 147);