C₁₉×#10635 #18016594

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10631
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#10635

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#124
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 294 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(25,27)(28,29,33,38,34,39,32,37)(30,40,43,35,44,51,42,52)(31,45,47,53,48,54,49,36)(41,56,57,59,46,50,58,55);(21,25)(23,26)(24,27)(28,30,34,44)(29,35,39,52)(31,46,48,41)(32,43,33,42)(36,50,53,56)(37,51,38,40)(45,59,54,55)(47,57,49,58);(20,21)(22,24)(23,27)(25,26)(28,31,32,47,34,48,33,49)(29,36,37,45,39,53,38,54)(30,41,42,57,44,46,43,58)(35,50,40,55,52,56,51,59)

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, 3623);