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C11×C3⋊(C49⋊AGL(1,𝔽5)) #44568395

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

Aliases

direct productC11×C3⋊(C49⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C11×C49⋊AGL(1,𝔽5))
unambiguous semidirect productC49⋊(C11×ΓL(1,𝔽16))

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C4
derived, HallC3×C5×C49 ⋊ C4×C11
HallC5×C11×C49 ⋊ Dic3
HallC3×C11×C49 ⋊ AGL(1,𝔽5)
HallC11×C49 ⋊ ΓL(1,𝔽16)
HallC5×C49 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ Dic49
HallC3×C49 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ Dic147
SylowC49 ⋊ C11×ΓL(1,𝔽16)
HallC3×C11 ⋊ C49⋊AGL(1,𝔽5)
HallC3×C5 ⋊ C11×Dic49
SylowC5 ⋊ C11×Dic147
SylowC3 ⋊ C11×C49⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C49⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C49C4×C11
FrattiniC7C11×C3⋊(C7⋊AGL(1,𝔽5))
FittingC3×C5×C11×C49C4
socleC3×C5×C7×C11Dic7
prime radicalC3×C7×D5×C11D7
cosocleC3×D5×C49C2×C11
LCSG ▷ C3×C5×C49
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3267 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 97);