Finite Group Databasebeta

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C32×C7×D275 #46831435

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

Aliases

direct productC32×C7×D275
unambiguous semidirect productC11⋊(C32×C7×D25)
unambiguous semidirect productC25⋊(C32×C7×D11)

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derived, HallC11×C25 ⋊ C2×C32×C7
HallC32×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ C2×C32
HallC32×C7×C25 ⋊ D11
HallC32×C7×C11 ⋊ D25
HallC32×C25 ⋊ C7×D11
HallC7×C25 ⋊ C32×D11
HallC32×C11 ⋊ C7×D25
HallC7×C11 ⋊ C32×D25
SylowC25 ⋊ C32×C7×D11
SylowC11 ⋊ C32×C7×D25

Subgroups

subgroupG/H
center, hypercenterC32×C7D275
commutator, cosocle, hypocenterC11×C25C2×C32×C7
FrattiniC5C32×C7×D55
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11D5
LCSG ▷ C11×C25
UCSC1 ◁ C32×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8757 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 78);