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C3×#18162 #10636769

order768
nilpotency class3
isoclinismisoclinic class of #18162
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC3×#18162

Subgroups

subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

1704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 48

A minimal faithful permutation representation — 4 generators on 19 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD3×#18162, #72252289
maximal subgroup ofD3×#18162, #72252289, C3×#346446, …
maximal normal subgroup ofD3×#18162, #72252289, C3×#346446
maximal quotient ofC3×#10767815, C3×#234591

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 11150);