C₁₉×#10614 #18016573

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10611
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#10614

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#126
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

276 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 2432

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

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, 3602);