Finite Group Databasebeta

← Prev (#44568321) Next (#44568323) →

C49×C3⋊(Dic11⋊C5) #44568322

order32340
automorphism?
homologyAbelianization (H1) = C4×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×C3⋊(Dic11⋊C5)
unambiguous semidirect productC3⋊(C49×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(Dic3×C49)
unambiguous semidirect productDic33⋊(C5×C49)
unambiguous semidirect product(C49×Dic33)⋊C5

Splittings

derived, HallC3×C11 ⋊ C4×C5×C49
HallC3×C49×C11⋊C5 ⋊ C4
HallC49×Dic33 ⋊ C5
HallC49×C11⋊C5 ⋊ Dic3
HallC3×C11×C49 ⋊ C4×C5
HallC11×C49 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ C4×C49
HallC3×C49 ⋊ Dic11⋊C5
HallDic33 ⋊ C5×C49
HallC11⋊C5 ⋊ Dic3×C49
SylowC11 ⋊ C5×Dic3×C49
SylowC3 ⋊ C49×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C49C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C4×C5×C49
FrattiniC2×C7C7×C3⋊AGL(1,𝔽11)
FittingC2×C3×C11×C49C2×C5
socle, cosocleC2×C3×C7×C11C2×C5×C7
prime radicalC2×C3×C7×C11⋊C5C2×C7
LCSG ▷ C3×C11
UCSC1 ◁ C2×C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6468

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 24);