Finite Group Databasebeta

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C3×#47796 #10666403

order768
nilpotency class2
isoclinismisoclinic class of #46350
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C28

Aliases

direct productC3×#47796

Subgroups

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

2622 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)(5,7)(16,17)(18,21)(19,20)(22,23);(8,9)(10,14)(11,12)(13,15)(17,19)(18,22);(4,5)(6,7)(9,12)(13,14)(16,17,20,19)(18,23,22,21);(8,9)(10,13)(11,12)(14,15)(16,18,20,22)(17,21,19,23);(8,10,11,15)(9,13,12,14)(16,19,20,17)(18,23,22,21)

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD3×#47796, #72253610
maximal subgroup ofD3×#47796, #72253610, C3×#7918389
maximal normal subgroup ofD3×#47796, #72253610, C3×#7918389
maximal quotient ofC3×#581603

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 40784);