Finite Group Databasebeta

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C3×#46367 #10664974

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

Aliases

direct productC3×#46367

Subgroups

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

2838 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)(8,9,12,10)(11,14,15,13);(9,10)(13,14)(16,17)(18,22)(19,20)(21,23);(4,5)(6,7)(17,20)(21,22);(8,10,12,9)(11,14,15,13)(16,17)(18,21)(19,20)(22,23);(8,11,12,15)(9,13,10,14)(16,18)(17,21)(19,23)(20,22)

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD3×#46367, #72253677
maximal subgroup ofD3×#46367, #72253677, C3×#7918389
maximal normal subgroup ofD3×#46367, #72253677, C3×#7918389
maximal quotient ofC3×#4312024

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 39355);