C₁₉×#13079 #18019038

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13079

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₁₉×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

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

normal subgroups only

This group has 486 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) = 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)(20,21,26,29,25,31,42,30)(22,32,28,41,35,46,34,24)(23,27,38,44,37,45,39,48)(33,50,43,36,51,49,47,40);(20,22,24,21,26,34,32,30,25,35,41,31,42,28,46,29)(23,33,40,27,39,43,49,44,37,51,36,45,38,47,50,48);(20,23)(21,27)(22,33)(24,40)(25,37)(26,39)(28,47)(29,48)(30,44)(31,45)(32,49)(34,43)(35,51)(36,41)(38,42)(46,50)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6067);