Finite Group Databasebeta

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C32×C7×C11×D25 #46831434

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C7×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×C11×D25
unambiguous semidirect productC25⋊(C2×C32×C7×C11)

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derived, SylowC25 ⋊ C2×C32×C7×C11
HallC32×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ C2×C32
HallC32×C7×C25 ⋊ C2×C11
HallC11×C25 ⋊ C2×C32×C7
HallC32×C25 ⋊ C2×C7×C11
HallC7×C25 ⋊ C2×C32×C11

Subgroups

subgroupG/H
center, hypercenterC32×C7×C11D25
commutator, cosocle, hypocenterC25C2×C32×C7×C11
FrattiniC5C32×C7×D5×C11
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11D5
LCSG ▷ C25
UCSC1 ◁ C32×C7×C11

144 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, 77);