C₁₉×#32898 #18038857

order	4864
nilpotency class	3
isoclinism	isoclinic class of #32898
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁹

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

4360 conjugacy classes of subgroups; only the 370 normal subgroups are shown.

normal subgroups only

This group has 4360 conjugacy classes of subgroups — too many to draw. Only its 370 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 31 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(28,31);(24,25)(26,28)(27,29)(30,31);(24,26)(25,28)(27,30)(29,31);(21,23)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 25886);