C₁₉×#9335 #18015294

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9331
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#9335

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

400 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 114 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)(20,21,23,27,25,29,24,28)(22,30,31,26,32,34,33,35)(36,37)(38,47,50,58)(39,51)(40,45)(41,55)(42,46)(43,49,59,54)(44,52)(48,63,66,57)(53,60)(56,61)(62,64,67,65);(20,22)(21,26,29,35)(23,31)(24,33)(25,32)(27,34,28,30)(36,38,40,54,42,50,41,49)(37,43,45,58,46,59,55,47)(39,48,52,65,53,66,56,64)(44,57,60,67,61,63,51,62);(21,27)(23,24)(26,34)(28,29)(30,35)(31,33)(36,39)(37,44)(38,48)(40,52)(41,56)(42,53)(43,57)(45,60)(46,61)(47,62)(49,64)(50,66)(51,55)(54,65)(58,67)(59,63)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 2323);