C₁₉×#13717 #18019676

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13717
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#13717

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2233
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#2218	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂×C₁₉×M₃₂ ◁ G

170 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 66 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)(21,26)(22,30)(23,33)(24,36)(27,39)(28,44)(29,45)(31,46)(32,50)(34,40)(35,41)(37,49)(38,42)(43,51)(47,48);(22,31)(26,39)(30,46)(32,41)(34,47)(40,48)(42,45)(44,51);(20,21,24,38,25,27,36,29)(22,32,34,44,31,41,47,51)(23,35,33,28,37,50,49,43)(26,40,45,30,39,48,42,46)

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, 6705);