C₁₉×#12405 #18018364

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12405

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 ◁ C₈×Q₈×C₁₉ ◁ G

276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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)(37,42)(38,41)(39,46)(43,51)(44,50)(45,48)(47,49);(20,22,26,23)(21,27,30,35)(24,33,25,32)(28,34,29,31)(36,37)(38,43)(39,47)(40,44)(41,49)(42,46)(45,50)(48,51);(20,23,26,22)(21,27,30,35)(24,32,25,33)(28,34,29,31)(36,38,40,41)(37,43,44,49)(39,45,48,46)(42,47,50,51)

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, 5393);