C₂×C₁₉×#2029 #18029424

order	4864
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₂×C₁₉×#2029

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁶×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

2818 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

normal subgroups only

This group has 2818 conjugacy classes of subgroups — too many to draw. Only its 350 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) = 37
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4,6,9)(5,11,12,8)(7,10,14,16)(13,17,18,15);(3,5,6,12)(4,8,9,11)(7,13,14,18)(10,15,16,17);(8,15)(11,17)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 16453);