Finite Group Databasebeta

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C7×C9×C11×D25 #46831365

order34650
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×C11×D25
unambiguous semidirect productC25⋊(C2×C7×C9×C11)

Splittings

Fitting, HallC7×C9×C11×C25 ⋊ C2
derived, SylowC25 ⋊ C2×C7×C9×C11
HallC9×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ C2×C9
HallC7×C9×C25 ⋊ C2×C11
HallC11×C25 ⋊ C2×C7×C9
HallC9×C25 ⋊ C2×C7×C11
HallC7×C25 ⋊ C2×C9×C11

Subgroups

subgroupG/H
center, hypercenterC7×C9×C11D25
commutator, hypocenterC25C2×C7×C9×C11
FrattiniC3×C5C3×C7×D5×C11
FittingC7×C9×C11×C25C2
socleC3×C5×C7×C11C3×D5
prime radicalC3×C7×C11×D25C3
cosocleC3×C25C2×C3×C7×C11
LCSG ▷ C25
UCSC1 ◁ C7×C9×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

9702 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 8);