Finite Group Databasebeta

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C25×C3⋊D231 #46831449

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

Aliases

direct productC25×C3⋊D231
unambiguous semidirect productC3⋊(C25×D231)
unambiguous semidirect productC7⋊(C25×C3⋊D33)

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derived, HallC32×C7×C11 ⋊ C2×C25
HallC32×C11×C25 ⋊ D7
HallC7×C11×C25 ⋊ C3⋊D3
HallC32×C7×C25 ⋊ D11
HallC11×C25 ⋊ C3⋊D21
HallC32×C25 ⋊ D77
HallC7×C25 ⋊ C3⋊D33
HallC32×C11 ⋊ D7×C25
HallC7×C11 ⋊ C3⋊D3×C25
HallC32×C7 ⋊ D11×C25
SylowC11 ⋊ C25×C3⋊D21
SylowC32 ⋊ C25×D77
SylowC7 ⋊ C25×C3⋊D33

Subgroups

subgroupG/H
center, hypercenterC25C3⋊D231
commutator, hypocenterC32×C7×C11C2×C25
FrattiniC5C5×C3⋊D231
FittingC32×C7×C11×C25C2
socle, cosocleC32×C5×C7×C11C2×C5
prime radicalC5×C3⋊D231C5
LCSG ▷ C32×C7×C11
UCSC1 ◁ C25

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 92);