Finite Group Databasebeta

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C3×#73779 #11808890

order1152
isoclinismisoclinic class of #4656
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C23

Aliases

direct productC3×#73779

Splittings

FittingC32×C4×C4⋊C4 ⋊ C2
SylowC32 ⋊ #2401

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2401
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

961 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 42901);