Finite Group Databasebeta

← Prev (#45688972) Next (#45688974) →

C3×C11⋊(Dic23⋊C11) #45688973

order33396
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊(Dic23⋊C11)
unambiguous semidirect productC11⋊(C3×Dic23⋊C11)
unambiguous semidirect product(C23⋊C11)⋊(C3×Dic11)
unambiguous semidirect productDic253⋊(C3×C11)
unambiguous semidirect product(C3×Dic253)⋊C11

Splittings

derivedC11×C23 ⋊ C3×C4×C11
HallC3×C11×C23⋊C11 ⋊ C4
HallC11×C23⋊C11 ⋊ C3×C4
HallC3×C23 ⋊ C11×Dic11
SylowC23 ⋊ C3×C11×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊AGL(1,𝔽23)
commutator, hypocenterC11×C23C3×C4×C11
FrattiniC2C3×C11⋊AGL(1,𝔽23)
Fitting, socleC2×C3×C11×C23C2×C11
prime radicalC2×C3×C11×C23⋊C11C2
cosocleC2×C11×C23C2×C3×C11
LCSG ▷ C11×C23
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3036

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 37);