Finite Group Databasebeta

← Prev (#44568393) Next (#44568395) →

C49×C3⋊(C11⋊AGL(1,𝔽5)) #44568394

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

Aliases

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

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C4
derived, HallC3×C5×C11 ⋊ C4×C49
HallC5×C11×C49 ⋊ Dic3
HallC3×C11×C49 ⋊ AGL(1,𝔽5)
HallC3×C5×C49 ⋊ Dic11
HallC11×C49 ⋊ ΓL(1,𝔽16)
HallC5×C49 ⋊ Dic33
HallC3×C49 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ Dic3×C49
HallC3×C11 ⋊ AGL(1,𝔽5)×C49
HallC3×C5 ⋊ Dic11×C49
SylowC11 ⋊ C49×ΓL(1,𝔽16)
SylowC5 ⋊ C49×Dic33
SylowC3 ⋊ C49×C11⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC49C3⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C11C4×C49
FrattiniC7C7×C3⋊(C11⋊AGL(1,𝔽5))
FittingC3×C5×C11×C49C4
socleC3×C5×C7×C11C4×C7
prime radical, cosocleC3×C7×D5×C11C2×C7
LCSG ▷ C3×C5×C11
UCSC1 ◁ C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3381 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 96);