Finite Group Databasebeta

← Prev (#44568378) Next (#44568380) →

C3×C11×C49⋊AGL(1,𝔽5) #44568379

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

Aliases

direct productC3×C11×C49⋊AGL(1,𝔽5)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C4
derived, HallC5×C49 ⋊ C3×C4×C11
HallC5×C11×C49 ⋊ C3×C4
HallC3×C11×C49 ⋊ AGL(1,𝔽5)
HallC3×C5×C49 ⋊ C4×C11
HallC11×C49 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C11 ⋊ Dic49
HallC3×C49 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ C3×Dic49
SylowC49 ⋊ C3×C11×AGL(1,𝔽5)
HallC3×C5 ⋊ C11×Dic49
SylowC5 ⋊ C3×C11×Dic49

Subgroups

subgroupG/H
center, hypercenterC3×C11C49⋊AGL(1,𝔽5)
commutator, hypocenterC5×C49C3×C4×C11
FrattiniC7C3×C11×C7⋊AGL(1,𝔽5)
FittingC3×C5×C11×C49C4
socleC3×C5×C7×C11Dic7
prime radicalC3×C7×D5×C11D7
cosocleD5×C49C2×C3×C11
LCSG ▷ C5×C49
UCSC1 ◁ C3×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3333 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 81);