C₁₉×#13330 #18019289

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13330

Subgroups

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

558 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 146 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) = 4864

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

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6318);