Finite Group Databasebeta

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C7⋊C9×D275 #46831388

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

Aliases

direct productC7⋊C9×D275
unambiguous semidirect productC11⋊(D25×C7⋊C9)
unambiguous semidirect productC25⋊(D11×C7⋊C9)
unambiguous semidirect product(C7×D275)⋊C9

Splittings

derived, HallC7×C11×C25 ⋊ C2×C9
HallC11×C25×C7⋊C9 ⋊ C2
HallC7×D275 ⋊ C9
HallC25×C7⋊C9 ⋊ D11
HallC11×C7⋊C9 ⋊ D25
HallC11×C25 ⋊ C2×C7⋊C9
HallC7×C25 ⋊ C9×D11
HallC7×C11 ⋊ C9×D25
SylowC25 ⋊ D11×C7⋊C9
SylowC11 ⋊ D25×C7⋊C9
SylowC7 ⋊ C9×D275

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D275
commutator, hypocenterC7×C11×C25C2×C9
FrattiniC3×C5ΓL(1,𝔽8)×D55
Fitting, cosocleC3×C7×C11×C25C2×C3
socleC3×C5×C7×C11C3×D5
prime radicalC3×C7×D275C3
LCSG ▷ C7×C11×C25
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

2085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 31);