C₁₉×#8477 #18014436

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#8477

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#535	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

682 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 1216

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)(20,21,23,27,24,26,32,34)(22,28,29,35,30,25,31,33)(36,37)(38,46)(39,50,52,43)(40,53)(41,45)(42,48)(44,56)(47,62,64,67)(49,60)(51,59,55,61)(54,58)(57,63,66,65);(20,22,24,30)(21,25,26,28)(23,31,32,29)(27,35,34,33)(36,38,41,49)(37,42,45,58)(39,47,52,64)(40,54,56,48)(43,57,50,66)(44,60,53,46)(51,65,55,63)(59,62,61,67);(21,26)(23,32)(25,28)(29,31)(36,39)(37,43)(38,47)(40,55)(41,52)(42,57)(44,61)(45,50)(46,62)(48,65)(49,64)(51,56)(53,59)(54,63)(58,66)(60,67)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1465);