Finite Group Databasebeta

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C121×C22⋊(C19⋊C3) #42119935

order27588
automorphism?
homologyAbelianization (H1) = C3×C121 · Schur multiplier (H2) = C2

Aliases

direct productC121×C22⋊(C19⋊C3)
unambiguous semidirect productC22⋊(C19⋊C3×C121)
unambiguous semidirect productC19⋊(A4×C121)
unambiguous semidirect product(C22×C121)⋊(C19⋊C3)
unambiguous semidirect product(C19×C121)⋊A4

Splittings

Fitting, HallC22×C19×C121 ⋊ C3
derived, HallC22×C19 ⋊ C3×C121
HallC19×C121 ⋊ A4
HallC22×C121 ⋊ C19⋊C3
SylowC19 ⋊ A4×C121
SylowC22 ⋊ C19⋊C3×C121

Subgroups

subgroupG/H
center, hypercenterC121C22⋊(C19⋊C3)
commutator, hypocenterC22×C19C3×C121
FrattiniC11C11×C22⋊(C19⋊C3)
FittingC22×C19×C121C3
socle, cosocleC22×C11×C19C3×C11
prime radicalC11×C22⋊(C19⋊C3)C11
LCSG ▷ C22×C19
UCSC1 ◁ C121

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9196

Conjugacy classes & character table

3388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 27);