C₁₉×#12438 #18018397

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

Aliases

direct product

C₁₉×#12438

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1667
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#2213	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 224 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)(23,36)(24,37)(27,38)(29,43)(30,42)(32,33)(34,49)(35,44)(39,45)(40,41)(46,47)(50,51);(20,21,27,43,24,29,23,26,25,30,36,41,37,40,38,42)(22,28,44,50,33,46,32,39,35,48,31,45,34,47,49,51);(20,22)(21,28)(23,32)(24,33)(25,35)(26,39)(27,44)(29,46)(30,48)(31,36)(34,37)(38,49)(40,47)(41,45)(42,51)(43,50)

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, 5426);