C₁₉×#13340 #18019299

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13340
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13340

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#493
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#2011
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#97 ◁ G

552 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 118 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)(22,33)(23,30)(24,29)(25,43)(26,31)(27,34)(28,35)(32,39)(36,45)(37,51)(38,48)(40,50)(41,46)(42,49)(44,47);(20,22)(21,27)(23,38)(24,34)(25,44)(26,37)(28,43)(29,47)(30,33)(31,46)(32,48)(35,40)(36,39)(41,42)(45,49)(50,51);(20,22)(21,28)(23,35)(24,41)(25,44)(26,37)(27,32)(29,33)(30,45)(31,48)(34,42)(36,39)(38,40)(43,46)(47,50)(49,51)

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, 6328);