Finite Group Databasebeta

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C3×#71570 #11773292

order1152
isoclinismisoclinic class of #4656
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×#71570

Splittings

FittingC22×C32×C4⋊C4 ⋊ C2
SylowC32 ⋊ #1439

Subgroups

subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC22×C32×C4⋊C4C2
socleC24×C32C23
prime radicalC24×C3×D3C22
cosocleC24×C3C23×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C3×#1439
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

1769 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, 7303);