C₁₉×#12351 #18018310

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12351

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₂×D₄×C₁₉	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#436 ◁ G

286 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 2432

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

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, 5339);