Finite Group Databasebeta

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C2×C3×A4×M16 #11919776

order1152
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C3×A4×M16
unambiguous semidirect product(C23×M16)⋊C32
unambiguous semidirect product(C23×C3×M16)⋊C3

Splittings

FittingC23×C3×M16 ⋊ C3
SylowC23×M16 ⋊ C32

Subgroups

subgroupG/H
centerC2×C3×C4C22×A4
commutatorC23C22×C32×C4
FrattiniC4C23×C3×A4
FittingC23×C3×M16C3
socleC24×C3C2×C3×C4
prime radicalC23×C3×A4C4
cosocleC22×C4C23×C32
hypercenterC2×C3×M16A4
hypocenterC22C2×C32×M16
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×M16

936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153787);