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C3×C49×C11⋊AGL(1,𝔽5) #44568378

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C4
derived, HallC5×C11 ⋊ C3×C4×C49
HallC5×C11×C49 ⋊ C3×C4
HallC3×C11×C49 ⋊ AGL(1,𝔽5)
HallC3×C5×C49 ⋊ Dic11
HallC11×C49 ⋊ C3×AGL(1,𝔽5)
HallC5×C49 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ C4×C49
HallC3×C11 ⋊ AGL(1,𝔽5)×C49
HallC3×C5 ⋊ Dic11×C49
SylowC11 ⋊ C3×AGL(1,𝔽5)×C49
SylowC5 ⋊ C3×Dic11×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4×C49
FrattiniC7C3×C7×C11⋊AGL(1,𝔽5)
FittingC3×C5×C11×C49C4
socleC3×C5×C7×C11C4×C7
prime radicalC3×C7×D5×C11C2×C7
cosocleC7×D5×C11C2×C3×C7
LCSG ▷ C5×C11
UCSC1 ◁ C3×C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3675 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 80);