C₁₉×#11913 #18017872

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11913

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1530
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	#97	C₂³×C₁₉
prime radical	C₁₉×#3176	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

296 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 94 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 — 3 generators on 51 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4901);