C₁₉×#12174 #18018133

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12173
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12174

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1598
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₁₉×#575	C₂²
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 340 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)(22,32)(23,37)(24,28)(25,30)(26,31)(27,33)(29,39)(34,45)(35,48)(36,49)(38,42)(40,46)(41,47)(43,51)(44,50);(20,22,26,36)(21,27,31,44)(23,38,40,51)(24,35,25,34)(28,42,30,43)(29,45,47,48)(32,46,49,37)(33,41,50,39);(21,28,31,30)(27,42,44,43)(29,46,47,37)(32,45,49,48)

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, 5162);