C₁₉×#12436 #18018395

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12436

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1667
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

234 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 74 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)(21,26)(22,31)(23,27)(24,36)(29,47)(30,41)(32,33)(34,48)(35,49)(37,42)(38,43)(39,40)(44,45)(50,51);(20,21,27,40,24,29,37,41,25,30,42,47,36,39,23,26)(22,28,31,43,33,44,48,51,35,46,49,50,34,45,32,38);(20,22)(21,28)(23,32)(24,33)(25,35)(26,38)(27,31)(29,44)(30,46)(34,36)(37,48)(39,45)(40,43)(41,51)(42,49)(47,50)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5424);