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C11×C49×ΓL(1,𝔽16) #44568393

order32340
automorphism?
homologyAbelianization (H1) = C4×C11×C49 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C4
derived, HallC3×C5 ⋊ C4×C11×C49
HallC5×C11×C49 ⋊ Dic3
HallC3×C11×C49 ⋊ AGL(1,𝔽5)
HallC3×C5×C49 ⋊ C4×C11
HallC5×C49 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ C4×C49
HallC3×C49 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ Dic3×C49
HallC3×C11 ⋊ AGL(1,𝔽5)×C49
SylowC5 ⋊ C11×Dic3×C49
SylowC3 ⋊ C11×AGL(1,𝔽5)×C49

Subgroups

subgroupG/H
center, hypercenterC11×C49ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C11×C49
FrattiniC7C7×C11×ΓL(1,𝔽16)
FittingC3×C5×C11×C49C4
socleC3×C5×C7×C11C4×C7
prime radicalC3×C7×D5×C11C2×C7
cosocleC3×C7×D5C2×C7×C11
LCSG ▷ C3×C5
UCSC1 ◁ C11×C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4851 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 95);