Finite Group Databasebeta

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C7×C11×C3⋊D75 #46831450

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

Aliases

direct productC7×C11×C3⋊D75
unambiguous semidirect productC3⋊(C7×C11×D75)
unambiguous semidirect productC25⋊(C7×C11×C3⋊D3)

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derived, HallC32×C25 ⋊ C2×C7×C11
HallC32×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ C3⋊D3
HallC32×C7×C25 ⋊ C2×C11
HallC32×C7×C11 ⋊ D25
HallC11×C25 ⋊ C7×C3⋊D3
HallC7×C25 ⋊ C11×C3⋊D3
HallC32×C11 ⋊ C7×D25
HallC32×C7 ⋊ C11×D25
SylowC25 ⋊ C7×C11×C3⋊D3
SylowC32 ⋊ C7×C11×D25

Subgroups

subgroupG/H
center, hypercenterC7×C11C3⋊D75
commutator, cosocle, hypocenterC32×C25C2×C7×C11
FrattiniC5C7×C11×C3⋊D15
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11D5
LCSG ▷ C32×C25
UCSC1 ◁ C7×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8778 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 93);