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C11×AGL(1,𝔽5)×C49⋊C3 #44568353

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×AGL(1,𝔽5)×C49⋊C3
unambiguous semidirect product(AGL(1,𝔽5)×C49)⋊(C3×C11)
unambiguous semidirect product(C11×AGL(1,𝔽5)×C49)⋊C3

Splittings

Fitting, HallC5×C11×C49 ⋊ C3×C4
derived, HallC5×C49 ⋊ C3×C4×C11
HallC11×AGL(1,𝔽5)×C49 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C4
HallAGL(1,𝔽5)×C49 ⋊ C3×C11
HallC5×C49⋊C3 ⋊ C4×C11
HallC11×C49 ⋊ C3×AGL(1,𝔽5)
HallC5×C11 ⋊ C4×C49⋊C3
SylowC49 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C4×C11×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC11AGL(1,𝔽5)×C49⋊C3
commutator, hypocenterC5×C49C3×C4×C11
FrattiniC7C11×AGL(1,𝔽5)×ΓL(1,𝔽8)
FittingC5×C11×C49C3×C4
socleC5×C7×C11C4×ΓL(1,𝔽8)
prime radicalD5×C11×C49⋊C3C2
cosocleD5×C49C2×C3×C11
LCSG ▷ C5×C49
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

1045 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 55);