Finite Group Databasebeta

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C3×#39885 #10658492

order768
nilpotency class2
isoclinismisoclinic class of #37644
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C28

Aliases

direct productC3×#39885

Subgroups

subgroupG/H
center, socleC23×C3C25
commutator, Frattini, cosocleC23C25×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

2858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 192

A minimal faithful permutation representation — 5 generators on 23 points:

(1,2,3)(4,5,6,7)(8,9,12,11)(10,14,15,13);(9,11)(13,14)(17,21)(19,22);(4,5)(6,7)(16,17)(18,22)(19,23)(20,21);(8,10,12,15)(9,13,11,14)(16,18,20,23)(17,22,21,19);(8,11,12,9)(10,14,15,13)(16,19,20,22)(17,23,21,18)

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD3×#39885, #72270675
maximal subgroup ofD3×#39885, #72270675, C3×#7659307
maximal normal subgroup ofD3×#39885, #72270675, C3×#7659307
maximal quotient ofC3×#647667

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 32873);