Finite Group Databasebeta

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C19×C3⋊(C11⋊#261) #45656792

order32604
automorphism?
homologyAbelianization (H1) = C4×C19 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C11×C13×C19 ⋊ C4
derived, HallC3×C11×C13 ⋊ C4×C19
HallC11×C13×C19 ⋊ Dic3
HallC3×C13×C19 ⋊ Dic11
HallC3×C11×C19 ⋊ #261
HallC13×C19 ⋊ Dic33
HallC11×C19 ⋊ C3⋊#261
HallC11×C13 ⋊ Dic3×C19
HallC3×C19 ⋊ C11⋊#261
HallC3×C13 ⋊ C19×Dic11
HallC3×C11 ⋊ C19×#261
SylowC13 ⋊ C19×Dic33
SylowC11 ⋊ C19×C3⋊#261
SylowC3 ⋊ C19×C11⋊#261

Subgroups

subgroupG/H
center, hypercenterC19C3⋊(C11⋊#261)
commutator, hypocenterC3×C11×C13C4×C19
FrattiniC1G
Fitting, socleC3×C11×C13×C19C4
prime radicalC3×C11×C19×D13C2
cosocleC3×C11×D13C2×C19
LCSG ▷ C3×C11×C13
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8151

Conjugacy classes & character table

2565 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 142);