C₁₉×#7477 #18013436

order	4864
nilpotency class	5
isoclinism	isoclinic class of #1418
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7477

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#357
commutator	C₁₆	C₄²×C₁₉
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₉
prime radical	C₂³×C₁₉	D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 178 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)(24,25,28,34)(26,38,40,46)(27,43,45,35)(29,33,47,42)(30,41,48,55)(31,39,32,37)(36,51,53,44)(49,54,50,52);(24,26,29,41,30,42,38,25,32,35,50,36,51,52,45,39,28,40,47,55,48,33,46,34,31,43,49,53,44,54,27,37)

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, 465);