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C3×#10938 #10629545

order768
nilpotency class3
isoclinismisoclinic class of #1913
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×#10938

Subgroups

subgroupG/H
center, socleC22×C3#386
commutatorC23C2×C3×C42
Frattini, cosocleC25C23×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C25×C3 ◁ G

1234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 96

A minimal faithful permutation representation — 3 generators on 23 points:

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

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD3×#10938, #72258672
maximal subgroup ofD3×#10938, #72258672, C3×#417824
maximal normal subgroup ofD3×#10938, #72258672, C3×#417824

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 3926);