Finite Group Databasebeta

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C11⋊C5×C3⋊#1181 #34062342

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

Aliases

direct productC11⋊C5×C3⋊#1181
unambiguous semidirect productC3⋊(C11⋊C5×#1181)
unambiguous semidirect product(C11×C3⋊#1181)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C29 ⋊ C4×C5
HallC3×C29×C11⋊C5 ⋊ C4
HallC11×C3⋊#1181 ⋊ C5
HallC29×C11⋊C5 ⋊ Dic3
HallC11×C29 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ #1181
HallC3×C29 ⋊ C4×C11⋊C5
HallC3×C11 ⋊ C5×#1181
SylowC29 ⋊ Dic3×C11⋊C5
SylowC11 ⋊ C5×C3⋊#1181
SylowC3 ⋊ C11⋊C5×#1181

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C11×C29C4×C5
prime radicalC3×C11⋊C5×D29C2
cosocleC3×C11×D29C2×C5
LCSG ▷ C3×C11×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 957

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 35);