Finite Group Databasebeta

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C3×C11×C19⋊#261 #45656773

order32604
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C19⋊#261

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C11C19⋊#261
commutator, hypocenterC13×C19C3×C4×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C19C4
prime radicalC3×C11×C19×D13C2
cosocleC19×D13C2×C3×C11
LCSG ▷ C13×C19
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8151

Conjugacy classes & character table

2607 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 123);