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C3×#15763 #10634370

order768
nilpotency class2
isoclinismisoclinic class of #15257
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C42

Aliases

direct productC3×#15763

Subgroups

subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

2882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 384

A minimal faithful permutation representation — 4 generators on 23 points:

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

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#72271212, #72271231, D3×#15763
maximal subgroup of#72271212, #72271231, C3×#772780, …
maximal normal subgroup of#72271212, #72271231, C3×#772780, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 8751);