C₁₉×#7524 #18013483

order	4864
nilpotency class	6
isoclinism	isoclinic class of #7523
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7524

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1404
commutator	#125	C₂×C₄×C₁₉
Frattini, cosocle	#490	C₂²×C₁₉
prime radical	C₁₉×#127	D₄
LCS	G ▷ #125 ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#490 ◁ G

134 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 30 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 — 2 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)(23,34,36,27)(24,29)(25,28,38,46)(26,31,41,49)(32,48)(33,47,39,51)(35,42,50,43)(37,44,40,45);(20,22,24,32)(21,26,29,43)(23,35,37,31)(25,39,38,33)(27,30,45,48)(28,42,46,41)(34,51,44,47)(36,49,40,50)

Conjugacy classes & character table

361 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 512);