C₁₉×#8478 #18014437

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×#8478

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

656 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 150 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)(20,21,24,29,25,28,32,35)(22,27,30,34,23,26,31,33)(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);(20,22,25,23)(21,26,28,27)(24,31,32,30)(29,34,35,33)(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);(20,23,25,22)(21,27,28,26)(24,30,32,31)(29,33,35,34)(36,39,41,52)(37,43,45,50)(38,47,49,64)(40,55,56,51)(42,57,58,66)(44,61,53,59)(46,62,60,67)(48,65,54,63)

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, 1466);