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C9×C7⋊(D11⋊C25) #46831379

order34650
automorphism?
homologyAbelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC9×C7⋊(D11⋊C25)
unambiguous semidirect product(C11⋊C25)⋊(C9×D7)
unambiguous semidirect product(C9×D77)⋊C25

Splittings

derived, HallC7×C11 ⋊ C2×C9×C25
HallC7×C9×C11⋊C25 ⋊ C2
HallC9×C11⋊C25 ⋊ D7
HallC7×C11⋊C25 ⋊ C2×C9
HallC9×D77 ⋊ C25
HallC7×C9×C11 ⋊ C2×C25
HallC11⋊C25 ⋊ C9×D7
HallD77 ⋊ C9×C25
HallC9×C11 ⋊ D7×C25
HallC7×C9 ⋊ D11⋊C25
SylowC11 ⋊ C9×D7×C25
SylowC7 ⋊ C9×D11⋊C25

Subgroups

subgroupG/H
center, hypercenterC5×C9C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C9×C25
FrattiniC3×C5C3×C7⋊AGL(1,𝔽11)
FittingC5×C7×C9×C11C2×C5
socle, cosocleC3×C5×C7×C11C2×C3×C5
prime radicalC3×C5×D77C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C5×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

1440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 22);