C₁₉×#32874 #18038833

order	4864
nilpotency class	3
isoclinism	isoclinic class of #32873
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₉×#32874

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2840
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂⁴×C₁₉ ◁ G

688 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 186 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 — 4 generators on 51 points:

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

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 25862);