C₁₉×#12028 #18017987

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12028
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#12028

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#106
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	#106
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

210 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 2432

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5016);