C₁₉×#10648 #18016607

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10645
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#10648

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#126
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

236 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,27,25,29,23,28)(22,26,30,35,32,33,31,34)(36,37)(38,46,49,59)(39,43)(40,44)(41,45)(42,48,56,53)(47,62,50,61)(51,57)(52,58)(54,60)(55,64,66,63)(65,67);(20,22)(21,26)(23,31)(24,30)(25,32)(27,35)(28,34)(29,33)(36,38,41,49)(37,42,45,56)(39,50,52,47)(40,53,54,48)(43,55,58,66)(44,59,60,46)(51,63,65,64)(57,62,67,61);(21,27)(22,30)(23,24)(26,33)(28,29)(31,32)(36,39,40,51,41,52,54,65)(37,43,44,57,45,58,60,67)(38,47,48,63,49,50,53,64)(42,55,46,61,56,66,59,62)

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3636);