C₁₉×#13710 #18019669

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13709
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#13710

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2226
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#508	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

160 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6698);