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C3×#62983 #10681590

order768
nilpotency class2
isoclinismisoclinic class of D4×H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C26×C3 · Schur multiplier (H2) = C213

Aliases

direct productC3×#62983

Subgroups

subgroupG/H
center, socleC22×C3C26
commutator, Frattini, cosocleC22C26×C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ G

8054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 96

A minimal faithful permutation representation — 6 generators on 19 points:

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

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#72271804, #72271817, D3×#62983
maximal subgroup of#72271804, #72271817, C3×#6595772, …
maximal normal subgroup of#72271804, #72271817, C3×#6595772, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 55971);