C₁₉×#12338 #18018297

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

Aliases

direct product

C₁₉×#12338

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#3403	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#446 ◁ G

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

normal subgroups only

This group has 320 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)(21,24)(22,26)(25,27)(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);(22,26)(24,27)(28,30)(29,35)(31,40)(32,45)(33,49)(34,42)(36,51)(37,54)(38,52)(39,44)(41,46)(43,50)(47,59)(48,53)(55,57)(56,58);(20,21,23,25)(22,27,26,24)(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, 5326);