C₁₉×#12373 #18018332

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12373

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#3287	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

360 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 86 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)(20,21,24,27)(22,25,23,26)(28,29,34,38)(30,39,42,57)(31,36,33,48)(32,44,47,58)(35,50,53,41)(37,43,55,46)(40,56,49,54)(45,51,59,52);(21,25)(22,23)(26,27)(28,30)(29,35)(31,40)(32,45)(33,49)(34,42)(36,51)(37,54)(38,53)(39,44)(41,46)(43,50)(47,59)(48,52)(55,56)(57,58);(21,26)(22,23)(25,27)(28,31,34,33)(29,36,38,48)(30,40,42,49)(32,43,47,46)(35,51,53,52)(37,44,55,58)(39,56,57,54)(41,45,50,59)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5361);