Finite Group Databasebeta

← Prev (#34062363) Next (#34062365) →

C3×C11×#10596817 #34062364

order19140
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×#10596817

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C4
derived, HallC5×C29 ⋊ C3×C4×C11
HallC5×C11×C29 ⋊ C3×C4
HallC3×C11×C29 ⋊ Dic5
HallC3×C5×C29 ⋊ C4×C11
HallC11×C29 ⋊ C3×Dic5
HallC3×C5×C11 ⋊ #1181
HallC3×C29 ⋊ C11×Dic5
HallC5×C11 ⋊ C3×#1181
SylowC29 ⋊ C3×C11×Dic5
HallC3×C5 ⋊ C11×#1181
SylowC5 ⋊ C3×C11×#1181

Subgroups

subgroupG/H
center, hypercenterC3×C11#10596817
commutator, hypocenterC5×C29C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C29C4
prime radicalC3×C5×C11×D29C2
cosocleC5×D29C2×C3×C11
LCSG ▷ C5×C29
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

1419 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 57);