C₁₉×#12413 #18018372

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

Aliases

direct product

C₁₉×#12413

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#446 ◁ G

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

normal subgroups only

This group has 266 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) = 4864

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)(20,21,26,30)(22,31,23,34)(24,29,25,28)(27,33,35,32)(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);(20,22,26,23)(21,27,30,35)(24,33,25,32)(28,34,29,31)(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);(20,23,26,22)(21,27,30,35)(24,32,25,33)(28,34,29,31)(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, 5401);