C₁₉×#12115 #18018074

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12114
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12115

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₁₉×#2010	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 422 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)(22,30)(23,34)(24,39)(25,29)(26,31)(27,38)(28,37)(32,50)(33,47)(35,45)(36,46)(40,43)(41,49)(42,51)(44,48);(20,22,25,33)(21,26,29,41)(23,35,36,51)(24,40,37,32)(27,43,44,50)(28,45,39,42)(30,46,47,34)(31,48,49,38);(23,36)(31,49)(35,51)(38,48)

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, 5103);