Finite Group Databasebeta

← Prev (#29503240) Next (#29503242) →

C3×C23×Dic11⋊C5 #29503241

order15180
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×Dic11⋊C5
unambiguous semidirect productDic11⋊(C3×C5×C23)
unambiguous semidirect product(C11⋊C5)⋊(C3×C4×C23)
unambiguous semidirect product(C3×Dic11)⋊(C5×C23)
unambiguous semidirect product(C23×Dic11)⋊(C3×C5)
unambiguous semidirect product(C3×C23×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C3×C4×C5×C23
HallC3×C23×C11⋊C5 ⋊ C4
HallC3×C23×Dic11 ⋊ C5
HallC23×C11⋊C5 ⋊ C3×C4
HallC23×Dic11 ⋊ C3×C5
HallC3×C11×C23 ⋊ C4×C5
HallC11×C23 ⋊ C3×C4×C5
HallC3×C11⋊C5 ⋊ C4×C23
HallC3×Dic11 ⋊ C5×C23
HallC11⋊C5 ⋊ C3×C4×C23
HallDic11 ⋊ C3×C5×C23
HallC3×C11 ⋊ C4×C5×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23AGL(1,𝔽11)
commutator, hypocenterC11C3×C4×C5×C23
FrattiniC2C3×C23×AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C23C2×C5
prime radicalC2×C3×C23×C11⋊C5C2
cosocleC2×C11C2×C3×C5×C23
LCSG ▷ C11
UCSC1 ◁ C2×C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3036

Conjugacy classes & character table

1518 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 27);