C₁₉×#13692 #18019651

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13691
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13692

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2206
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 216 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)(21,25)(22,32)(23,26)(24,36)(28,42)(29,35)(30,31)(33,44)(34,49)(37,40)(38,46)(39,45)(41,48)(43,51)(47,50);(20,21,26,30,27,31,23,25)(22,28,41,47,34,43,33,40)(24,29,38,45,39,46,35,36)(32,37,44,51,49,50,48,42);(20,22)(21,28)(23,33)(24,37)(25,40)(26,41)(27,34)(29,44)(30,47)(31,43)(32,36)(35,42)(38,51)(39,50)(45,49)(46,48)

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, 6680);