Finite Group Databasebeta

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C7×C25×C3⋊D33 #46831447

order34650
automorphism?
homologyAbelianization (H1) = C2×C7×C25 · Schur multiplier (H2) = C3

Aliases

direct productC7×C25×C3⋊D33
unambiguous semidirect productC3⋊(C7×C25×D33)

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derived, HallC32×C11 ⋊ C2×C7×C25
HallC32×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ C3⋊D3
HallC32×C7×C25 ⋊ D11
HallC32×C7×C11 ⋊ C2×C25
HallC11×C25 ⋊ C7×C3⋊D3
HallC32×C25 ⋊ C7×D11
HallC7×C11 ⋊ C3⋊D3×C25
HallC32×C7 ⋊ D11×C25
SylowC11 ⋊ C7×C3⋊D3×C25
SylowC32 ⋊ C7×D11×C25

Subgroups

subgroupG/H
center, hypercenterC7×C25C3⋊D33
commutator, hypocenterC32×C11C2×C7×C25
FrattiniC5C5×C7×C3⋊D33
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11C2×C5
prime radicalC5×C7×C3⋊D33C5
cosocleC32×C5×C11C2×C5×C7
LCSG ▷ C32×C11
UCSC1 ◁ C7×C25

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 90);