Finite Group Databasebeta

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C3×C11⋊(C19⋊#261) #45656777

order32604
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C11×C13×C19 ⋊ C4
derived, HallC11×C13×C19 ⋊ C3×C4
HallC3×C13×C19 ⋊ Dic11
HallC3×C11×C19 ⋊ #261
HallC3×C11×C13 ⋊ Dic19
HallC13×C19 ⋊ C3×Dic11
HallC11×C19 ⋊ C3×#261
HallC11×C13 ⋊ C3×Dic19
HallC3×C19 ⋊ C11⋊#261
HallC3×C13 ⋊ Dic209
HallC3×C11 ⋊ C19⋊#261
SylowC19 ⋊ C3×C11⋊#261
SylowC13 ⋊ C3×Dic209
SylowC11 ⋊ C3×C19⋊#261

Subgroups

subgroupG/H
center, hypercenterC3C11⋊(C19⋊#261)
commutator, hypocenterC11×C13×C19C3×C4
FrattiniC1G
Fitting, socleC3×C11×C13×C19C4
prime radicalC3×C11×C19×D13C2
cosocleC11×C19×D13C2×C3
LCSG ▷ C11×C13×C19
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8151

Conjugacy classes & character table

2517 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 127);