Finite Group Databasebeta

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C3×#62912 #10681519

order768
nilpotency class2
isoclinismisoclinic class of #62892
automorphism?
homologyAbelianization (H1) = C26×C3 · Schur multiplier (H2) = C213

Aliases

direct productC3×#62912

Subgroups

subgroupG/H
center, socleC22×C3C26
commutator, Frattini, cosocleC22C26×C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ G

8078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 96

A minimal faithful permutation representation — 6 generators on 19 points:

(1,2,3)(5,8)(9,11)(12,13)(14,18)(15,16)(17,19);(13,16)(17,18);(4,5)(6,9)(7,8)(10,11)(12,13)(14,17)(15,16)(18,19);(6,10)(9,11)(12,14)(13,17)(15,19)(16,18);(4,6,7,10)(5,9,8,11);(4,5)(6,9)(7,8)(10,11)

Conjugacy classes & character table

219 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD3×#62912, #72272196
maximal subgroup ofC3×#10586472, D3×#62912, #72272196
maximal normal subgroup ofC3×#10586472, D3×#62912, #72272196

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 55900);