C₁₉×#9426 #18015385

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9415
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#9426

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

422 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 1216

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)(20,21,24,29,25,27,23,28)(22,30,33,26,32,35,31,34)(36,37,41,45,42,47,40,46)(38,48,51,58,52,61,50,43)(39,53,55,44,56,59,54,60)(49,57,64,66,65,67,63,62);(20,22)(21,26)(23,33)(24,31)(25,32)(27,34)(28,35)(29,30)(36,38)(37,43,47,58)(39,49)(40,50)(41,51)(42,52)(44,57,60,67)(45,48,46,61)(53,62,59,66)(54,63)(55,64)(56,65);(21,27)(23,24)(26,34)(31,33)(36,39,42,56)(37,44,47,60)(38,49,52,65)(40,55,41,54)(43,57,58,67)(45,53,46,59)(48,62,61,66)(50,64,51,63)

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, 2414);