C₁₉×#9190 #18015149

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9183
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#9190

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

436 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24,25,26)(28,29,33,37,34,38,32,48)(30,39,43,50,42,54,41,35)(31,44,46,52,47,36,45,51)(40,53,57,49,56,59,55,58);(20,21,22,26,23,25,27,24)(28,30,34,42)(29,35)(31,40,47,56)(32,41,33,43)(36,49)(37,39)(38,50)(44,58)(45,55,46,57)(48,54)(51,59)(52,53);(28,31,34,47)(29,36,38,44)(30,40,42,56)(32,46,33,45)(35,49,50,58)(37,52,48,51)(39,53,54,59)(41,57,43,55)

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, 2178);