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C3×(C11⋊C5)⋊#1181 #34062333

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

Aliases

direct productC3×(C11⋊C5)⋊#1181
unambiguous semidirect product(C11⋊C5)⋊(C3×#1181)
unambiguous semidirect product(C11⋊#1181)⋊(C3×C5)
unambiguous semidirect product(C3×C11⋊#1181)⋊C5

Splittings

Fitting, socle, HallC3×C11×C29 ⋊ C4×C5
derived, HallC11×C29 ⋊ C3×C4×C5
HallC3×C29×C11⋊C5 ⋊ C4
HallC3×C11⋊#1181 ⋊ C5
HallC29×C11⋊C5 ⋊ C3×C4
HallC11⋊#1181 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ #1181
HallC3×C29 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3×#1181
HallC3×C11 ⋊ C5×#1181
SylowC29 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C3×C5×#1181

Subgroups

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

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 957

Conjugacy classes & character table

213 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 26);