Finite Group Databasebeta

← Prev (#34062353) Next (#34062355) →

C3×C5×C11⋊#1181 #34062354

order19140
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11⋊#1181

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C4
derived, HallC11×C29 ⋊ C3×C4×C5
HallC5×C11×C29 ⋊ C3×C4
HallC3×C11×C29 ⋊ C4×C5
HallC3×C5×C29 ⋊ Dic11
HallC3×C5×C11 ⋊ #1181
HallC5×C29 ⋊ C3×Dic11
HallC3×C29 ⋊ C5×Dic11
HallC5×C11 ⋊ C3×#1181
HallC3×C11 ⋊ C5×#1181
SylowC29 ⋊ C3×C5×Dic11
SylowC11 ⋊ C3×C5×#1181

Subgroups

subgroupG/H
center, hypercenterC3×C5C11⋊#1181
commutator, hypocenterC11×C29C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C29C4
prime radicalC3×C5×C11×D29C2
cosocleC11×D29C2×C3×C5
LCSG ▷ C11×C29
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 47);