C₁₉×#12309 #18018268

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12307
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12309

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1616
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₁₉×#469	C₂²
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

280 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 70 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)(20,21,26,30,25,31,24,28)(22,32,34,49,36,50,35,46)(23,37,40,47,39,45,41,29)(27,42,43,33,44,38,48,51);(20,22)(21,27)(23,38)(24,34)(25,36)(26,35)(28,43)(29,46)(30,48)(31,44)(32,45)(33,40)(37,50)(39,42)(41,51)(47,49);(21,28,31,30)(23,39)(27,43,44,48)(29,45,47,37)(32,49,50,46)(33,51)(38,42)(40,41)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5297);