Finite Group Databasebeta

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C11×C3⋊(C19⋊#261) #45656785

order32604
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(C19⋊#261)
unambiguous semidirect productC3⋊(C11×C19⋊#261)
unambiguous semidirect productC19⋊(C11×C3⋊#261)

Splittings

Fitting, socle, HallC3×C11×C13×C19 ⋊ C4
derived, HallC3×C13×C19 ⋊ C4×C11
HallC11×C13×C19 ⋊ Dic3
HallC3×C11×C19 ⋊ #261
HallC3×C11×C13 ⋊ Dic19
HallC13×C19 ⋊ C11×Dic3
HallC11×C19 ⋊ C3⋊#261
HallC11×C13 ⋊ Dic57
HallC3×C19 ⋊ C11×#261
HallC3×C13 ⋊ C11×Dic19
HallC3×C11 ⋊ C19⋊#261
SylowC19 ⋊ C11×C3⋊#261
SylowC13 ⋊ C11×Dic57
SylowC3 ⋊ C11×C19⋊#261

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C19⋊#261)
commutator, hypocenterC3×C13×C19C4×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C19C4
prime radicalC3×C11×C19×D13C2
cosocleC3×C19×D13C2×C11
LCSG ▷ C3×C13×C19
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8151

Conjugacy classes & character table

2541 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 135);