C₁₉×#7267 #18013226

order	4864
nilpotency class	4
isoclinism	isoclinic class of #1355
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7267

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#329
commutator	C₄²	C₄²×C₁₉
Frattini, cosocle	C₂×#97	C₂²×C₁₉
socle	C₂×C₁₉	#1295
prime radical	C₂³×C₁₉	#101
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#97 ◁ G

196 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 82 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)(20,21,23,28,26,30,25,40)(22,31,32,27,34,41,35,43)(24,37,36,44,38,45,39,29)(33,48,47,46,50,42,49,51);(20,22,24,33,25,35,39,49,26,34,38,50,23,32,36,47)(21,27,29,42,28,41,37,51,30,43,44,48,40,31,45,46)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 255);