Finite Group Databasebeta

← Prev (#30634090) Next (#30634092) →

C3×C11×Dic123 #30634091

order16236
isoclinismisoclinic class of D123
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic123
unambiguous semidirect productC3⋊(C3×C11×Dic41)

Splittings

derivedC3×C41 ⋊ C3×C4×C11
HallC32×C11×C41 ⋊ C4
HallC11×C41 ⋊ C3×Dic3
HallC32×C41 ⋊ C4×C11
HallC32×C11 ⋊ Dic41
SylowC41 ⋊ C3×C11×Dic3
SylowC32 ⋊ C11×Dic41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D123
commutator, hypocenterC3×C41C3×C4×C11
FrattiniC2C3×C11×D123
Fitting, socle, prime radicalC2×C32×C11×C41C2
cosocleC2×C3×C41C2×C3×C11
LCSG ▷ C3×C41
UCSC1 ◁ C2×C3×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5412

Conjugacy classes & character table

4158 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16236, 34);