Finite Group Databasebeta

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C7×C9⋊(D11⋊C25) #46831381

order34650
automorphism?
homologyAbelianization (H1) = C2×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9⋊(D11⋊C25)
unambiguous semidirect productC9⋊(C7×D11⋊C25)
unambiguous semidirect productD99⋊(C7×C25)
unambiguous semidirect product(C11⋊C25)⋊(C7×D9)
unambiguous semidirect product(C7×D99)⋊C25

Splittings

derived, HallC9×C11 ⋊ C2×C7×C25
HallC7×C9×C11⋊C25 ⋊ C2
HallC9×C11⋊C25 ⋊ C2×C7
HallC7×C11⋊C25 ⋊ D9
HallC7×D99 ⋊ C25
HallC7×C9×C11 ⋊ C2×C25
HallC11⋊C25 ⋊ C7×D9
HallD99 ⋊ C7×C25
HallC7×C11 ⋊ D9×C25
HallC7×C9 ⋊ D11⋊C25
SylowC11 ⋊ C7×D9×C25
SylowC9 ⋊ C7×D11⋊C25

Subgroups

subgroupG/H
center, hypercenterC5×C7C9⋊AGL(1,𝔽11)
commutator, hypocenterC9×C11C2×C7×C25
FrattiniC3×C5C7×C3⋊AGL(1,𝔽11)
FittingC5×C7×C9×C11C2×C5
socleC3×C5×C7×C11C5×D3
prime radicalC5×C7×D99C5
cosocleC5×C9×C11C2×C5×C7
LCSG ▷ C9×C11
UCSC1 ◁ C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 24);