Finite Group Databasebeta

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C7×C3⋊D3×C11⋊C25 #46831411

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

Aliases

direct productC7×C3⋊D3×C11⋊C25
unambiguous semidirect productC3⋊(D3×C7×C11⋊C25)
unambiguous semidirect product(C11×C3⋊D3)⋊(C7×C25)
unambiguous semidirect product(C7×C11×C3⋊D3)⋊C25

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊D3×C11⋊C5
commutator, hypocenterC32×C11C2×C7×C25
FrattiniC5C7×C3⋊D3×C11⋊C5
Fitting, socleC32×C5×C7×C11C2×C5
prime radicalC5×C7×C11×C3⋊D3C5
cosocleC32×C5×C11C2×C5×C7
LCSG ▷ C32×C11
UCSC1 ◁ C5×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 54);