Finite Group Databasebeta

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C5×C3⋊(C11⋊#1181) #34062374

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

Aliases

direct productC5×C3⋊(C11⋊#1181)
unambiguous semidirect productC3⋊(C5×C11⋊#1181)

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C4
derived, HallC3×C11×C29 ⋊ C4×C5
HallC5×C11×C29 ⋊ Dic3
HallC3×C5×C29 ⋊ Dic11
HallC11×C29 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ #1181
HallC5×C29 ⋊ Dic33
HallC3×C29 ⋊ C5×Dic11
HallC5×C11 ⋊ C3⋊#1181
HallC3×C11 ⋊ C5×#1181
SylowC29 ⋊ C5×Dic33
HallC3×C5 ⋊ C11⋊#1181
SylowC11 ⋊ C5×C3⋊#1181
SylowC3 ⋊ C5×C11⋊#1181

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C11⋊#1181)
commutator, hypocenterC3×C11×C29C4×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C29C4
prime radicalC3×C5×C11×D29C2
cosocleC3×C11×D29C2×C5
LCSG ▷ C3×C11×C29
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

1335 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 67);