C₁₉×#7474 #18013433

order	4864
nilpotency class	5
isoclinism	isoclinic class of #1426
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7474

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#367
commutator	C₁₆	C₄²×C₁₉
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₉
prime radical	C₂³×C₁₉	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

174 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 55
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 2 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(25,31,32,47)(26,36)(27,41)(28,44)(29,38)(33,52,51,34)(35,55,48,50)(37,45)(39,43)(40,42)(46,53,54,49);(21,23)(24,25,27,33,28,34,26,31,38,48,36,49,37,46,41,55,30,32,43,51,45,52,40,47,29,35,42,53,44,54,39,50)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 462);