Finite Group Databasebeta

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C11×C49×C19⋊C3 #44502168

order30723
automorphism?
homologyAbelianization (H1) = C3×C11×C49 · Schur multiplier (H2) = C1

Aliases

direct productC11×C49×C19⋊C3
unambiguous semidirect productC19⋊(C3×C11×C49)
unambiguous semidirect product(C11×C19)⋊(C3×C49)

Splittings

Fitting, HallC11×C19×C49 ⋊ C3
derived, SylowC19 ⋊ C3×C11×C49
HallC19×C49 ⋊ C3×C11
HallC11×C19 ⋊ C3×C49

Subgroups

subgroupG/H
center, hypercenterC11×C49C19⋊C3
commutator, hypocenterC19C3×C11×C49
FrattiniC7C7×C11×C19⋊C3
FittingC11×C19×C49C3
socleC7×C11×C19C3×C7
prime radicalC7×C11×C19⋊C3C7
cosocleC7×C19C3×C7×C11
LCSG ▷ C19
UCSC1 ◁ C11×C49

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10241

Conjugacy classes & character table

4851 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30723, 2);