C₁₉×#12415 #18018374

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

Aliases

direct product

C₁₉×#12415

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

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

normal subgroups only

This group has 272 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) = 51
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 51 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)(37,41)(38,44)(39,47)(42,50)(43,51)(45,48)(46,49);(20,22,26,23)(21,27,30,35)(24,33,25,32)(28,34,29,31)(36,37,40,42)(38,45,46,51)(39,48,47,43)(41,49,50,44);(20,23,26,22)(21,27,30,35)(24,32,25,33)(28,34,29,31)(38,46)(41,50)(44,49)(45,51)

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, 5403);