C₁₉×#10385 #18016344

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10382
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#10385

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

396 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 1216

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

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, 3373);