C₁₉×#12116 #18018075

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

Aliases

direct product

C₁₉×#12116

Subgroups

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

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

normal subgroups only

This group has 426 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)(22,31)(23,28)(24,36)(25,40)(26,30)(27,33)(29,38)(32,47)(34,48)(35,46)(37,42)(39,51)(41,45)(43,50)(44,49);(20,22)(21,27)(23,32)(24,37)(25,41)(26,34)(28,42)(29,45)(30,43)(31,36)(33,38)(35,50)(39,49)(40,44)(46,47)(48,51);(20,23,26,25)(21,28,30,40)(22,32,34,41)(24,38,39,35)(27,42,43,44)(29,36,46,51)(31,47,48,45)(33,49,50,37)

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, 5104);