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C7×C11×(C5⋊D5)⋊C9 #46831493

order34650
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C11 · Schur multiplier (H2) = C5

Aliases

direct productC7×C11×(C5⋊D5)⋊C9
unambiguous semidirect product(C5⋊D5)⋊(C7×C9×C11)
unambiguous semidirect product(C11×C5⋊D5)⋊(C7×C9)

Splittings

derived, SylowC52 ⋊ C2×C7×C9×C11
HallC7×C11×C52⋊C9 ⋊ C2
HallC7×C11×C5⋊D5 ⋊ C9
HallC11×C52⋊C9 ⋊ C2×C7
HallC52×C7×C11 ⋊ C2×C9
HallC7×C52⋊C9 ⋊ C2×C11
HallC11×C5⋊D5 ⋊ C7×C9
HallC7×C5⋊D5 ⋊ C9×C11
HallC52×C11 ⋊ C2×C7×C9
HallC52⋊C9 ⋊ C2×C7×C11
HallC52×C7 ⋊ C2×C9×C11
HallC5⋊D5 ⋊ C7×C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11(C5⋊D5)⋊C3
commutator, hypocenterC52C2×C7×C9×C11
FrattiniC3C7×C11×(C5⋊D5)⋊C3
Fitting, socleC3×C52×C7×C11C2×C3
prime radicalC3×C7×C11×C5⋊D5C3
cosocleC3×C52C2×C3×C7×C11
LCSG ▷ C52
UCSC1 ◁ C3×C7×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 136);