Finite Group Databasebeta

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C11×C25⋊(D7⋊C9) #46831389

order34650
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25⋊(D7⋊C9)
unambiguous semidirect productC25⋊(C11×D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(C11×D25)
unambiguous semidirect productD175⋊(C9×C11)
unambiguous semidirect product(C11×D175)⋊C9

Splittings

derived, HallC7×C25 ⋊ C2×C9×C11
HallC11×C25×C7⋊C9 ⋊ C2
HallC11×D175 ⋊ C9
HallC7×C11×C25 ⋊ C2×C9
HallC25×C7⋊C9 ⋊ C2×C11
HallC11×C7⋊C9 ⋊ D25
HallD175 ⋊ C9×C11
HallC11×C25 ⋊ D7⋊C9
HallC7×C11 ⋊ C9×D25
HallC7⋊C9 ⋊ C11×D25
SylowC25 ⋊ C11×D7⋊C9
SylowC7 ⋊ C9×C11×D25

Subgroups

subgroupG/H
center, hypercenterC3×C11ΓL(1,𝔽8)⋊D25
commutator, hypocenterC7×C25C2×C9×C11
FrattiniC3×C5C11×C5⋊AGL(1,𝔽7)
FittingC3×C7×C11×C25C2×C3
socleC3×C5×C7×C11C3×D5
prime radicalC3×C11×D175C3
cosocleC3×C7×C25C2×C3×C11
LCSG ▷ C7×C25
UCSC1 ◁ C3×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

2211 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 32);