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C3×#36258 #10654865

order768
nilpotency class2
isoclinismisoclinic class of D4×#120
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productC3×#36258

Subgroups

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

3732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 192

A minimal faithful permutation representation — 5 generators on 19 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#72270681, D3×#36258
maximal subgroup of#72270681, D3×#36258, C3×#7659307
maximal normal subgroup of#72270681, D3×#36258, C3×#7659307
maximal quotient ofC3×#4306523

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 29246);