Finite Group Databasebeta

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A4×C23×C121 #45688963

order33396
automorphism?
homologyAbelianization (H1) = C3×C23×C121 · Schur multiplier (H2) = C2

Aliases

direct productA4×C23×C121
unambiguous semidirect productC22⋊(C3×C23×C121)
unambiguous semidirect product(C22×C121)⋊(C3×C23)
unambiguous semidirect product(C22×C23×C121)⋊C3

Splittings

Fitting, HallC22×C23×C121 ⋊ C3
derived, SylowC22 ⋊ C3×C23×C121
HallC22×C121 ⋊ C3×C23
HallC22×C23 ⋊ C3×C121

Subgroups

subgroupG/H
center, hypercenterC23×C121A4
commutator, hypocenterC22C3×C23×C121
FrattiniC11C11×A4×C23
FittingC22×C23×C121C3
socleC22×C11×C23C3×C11
prime radicalC11×A4×C23C11
cosocleC22×C11C3×C11×C23
LCSG ▷ C22
UCSC1 ◁ C23×C121

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11132

Conjugacy classes & character table

11132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 27);