Finite Group Databasebeta

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C52×C11⋊(D7⋊C9) #46831479

order34650
automorphism?
homologyAbelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC52×C11⋊(D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(C52×D11)

Splittings

derived, HallC7×C11 ⋊ C2×C52×C9
HallC52×C11×C7⋊C9 ⋊ C2
HallC52×D77 ⋊ C9
HallC52×C7×C11 ⋊ C2×C9
HallC52×C7⋊C9 ⋊ D11
HallC11×C7⋊C9 ⋊ C2×C52
HallC52×C11 ⋊ D7⋊C9
HallC52×C7 ⋊ C9×D11
HallD77 ⋊ C52×C9
HallC7⋊C9 ⋊ C52×D11
SylowC11 ⋊ C52×D7⋊C9
SylowC7 ⋊ C52×C9×D11

Subgroups

subgroupG/H
center, hypercenterC3×C52C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C2×C52×C9
FrattiniC3C52×C11⋊AGL(1,𝔽7)
Fitting, socleC3×C52×C7×C11C2×C3
prime radicalC3×C52×D77C3
cosocleC3×C7×C11C2×C3×C52
LCSG ▷ C7×C11
UCSC1 ◁ C3×C52

192 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, 122);