C₁₉×#13309 #18019268

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13309
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13309

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1999
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

568 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 114 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)(22,30)(23,34)(24,39)(25,28)(26,31)(27,37)(29,36)(32,46)(33,48)(35,45)(38,49)(40,43)(41,47)(42,50)(44,51);(20,22)(21,26)(23,35)(24,40)(25,32)(27,43)(28,41)(29,45)(30,34)(31,37)(33,36)(38,50)(39,42)(44,48)(46,49)(47,51);(26,41)(30,46)(42,45)(43,48)

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, 6297);