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C11×(C49⋊C3)⋊AGL(1,𝔽5) #44568351

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

Aliases

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

Splittings

Fitting, HallC5×C11×C49 ⋊ C3×C4
derived, HallC5×C49 ⋊ C3×C4×C11
HallC11×C49⋊AGL(1,𝔽5) ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C4
HallC11×C49⋊C3 ⋊ AGL(1,𝔽5)
HallC49⋊AGL(1,𝔽5) ⋊ C3×C11
HallC5×C49⋊C3 ⋊ C4×C11
HallC11×C49 ⋊ C3×AGL(1,𝔽5)
HallC49⋊C3 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ (C49⋊C3)⋊C4
SylowC49 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×(C49⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC11(C49⋊C3)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C49C3×C4×C11
FrattiniC7C11×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
FittingC5×C11×C49C3×C4
socleC5×C7×C11ΓL(1,𝔽8)⋊C4
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 53);