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C11×D49⋊C9 #23753250

order9702
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D49⋊C9
unambiguous semidirect productD49⋊(C9×C11)
unambiguous semidirect product(C49⋊C9)⋊(C2×C11)
unambiguous semidirect product(C11×D49)⋊C9

Splittings

derived, SylowC49 ⋊ C2×C9×C11
HallC11×C49⋊C9 ⋊ C2
HallC11×D49 ⋊ C9
HallC11×C49 ⋊ C2×C9
HallC49⋊C9 ⋊ C2×C11
HallD49 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11D49⋊C3
commutator, hypocenterC49C2×C9×C11
FrattiniC3×C7C11×AGL(1,𝔽7)
FittingC3×C11×C49C2×C3
socleC3×C7×C11AGL(1,𝔽7)
prime radicalC3×C11×D49C3
cosocleC3×C49C2×C3×C11
LCSG ▷ C49
UCSC1 ◁ C3×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

462 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×D49⋊C9, C2×C11×D49⋊C9
maximal normal subgroup ofD11×D49⋊C9, C2×C11×D49⋊C9
maximal quotient ofC11×Dic49⋊C9, C2×C11×D49⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9702, 3);