C₁₉×#12400 #18018359

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12400

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#3355	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#436 ◁ G

286 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 78 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)(20,21,25,29)(22,30,33,34)(23,28,24,27)(26,32,35,31)(36,37,41,45)(38,46,48,65)(39,50,52,64)(40,55,53,44)(42,57,58,47)(43,60,62,54)(49,66,56,61)(51,63,67,59);(20,22,25,33)(21,26,29,35)(23,32,24,31)(27,34,28,30)(36,38,41,48)(37,42,45,58)(39,51,52,67)(40,56,53,49)(43,61,62,66)(44,63,55,59)(46,64,65,50)(47,60,57,54);(21,27)(23,24)(26,34)(28,29)(30,35)(31,32)(39,52)(43,62)(46,65)(47,57)(50,64)(51,67)(54,60)(61,66)

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, 5388);