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C25×C11⋊(D7⋊C9) #46831386

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

Aliases

direct productC25×C11⋊(D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(D11×C25)
unambiguous semidirect product(C25×D77)⋊C9

Splittings

derived, HallC7×C11 ⋊ C2×C9×C25
HallC11×C25×C7⋊C9 ⋊ C2
HallC25×D77 ⋊ C9
HallC7×C11×C25 ⋊ C2×C9
HallC25×C7⋊C9 ⋊ D11
HallC11×C7⋊C9 ⋊ C2×C25
HallC11×C25 ⋊ D7⋊C9
HallC7×C25 ⋊ C9×D11
HallD77 ⋊ C9×C25
HallC7⋊C9 ⋊ D11×C25
SylowC11 ⋊ C25×D7⋊C9
SylowC7 ⋊ C9×D11×C25

Subgroups

subgroupG/H
center, hypercenterC3×C25C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C2×C9×C25
FrattiniC3×C5C5×C11⋊AGL(1,𝔽7)
FittingC3×C7×C11×C25C2×C3
socle, cosocleC3×C5×C7×C11C2×C3×C5
prime radicalC3×C5×D77C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

2400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 29);