C₁₉×#10217 #18016176

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10217

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 430 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) = 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)(22,29)(23,25)(24,34)(26,28)(27,30)(31,35)(32,33)(36,37,42,47)(38,48,51,62)(39,52,55,60)(40,46,41,45)(43,56,58,50)(44,53,61,54)(49,57,65,59)(63,66,67,64);(20,22,25,31)(21,27,23,33)(24,32,26,30)(28,35,34,29)(36,38,42,51)(37,43,47,58)(39,49,55,65)(40,56,41,50)(44,59,61,57)(45,62,46,48)(52,63,60,67)(53,66,54,64);(20,23,25,21)(22,29,31,35)(24,34,26,28)(27,30,33,32)(36,39,42,55)(37,44,47,61)(38,49,51,65)(40,54,41,53)(43,57,58,59)(45,52,46,60)(48,63,62,67)(50,66,56,64)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3205);