C₂×C₁₉×#2062 #18029522

order	4864
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₁₉×#2062

Subgroups

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

1614 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 1614 conjugacy classes of subgroups — too many to draw. Only its 382 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) = 1216

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);(3,4,7,9)(5,10,6,8)(11,12)(13,15)(14,16)(17,18);(3,5,7,6)(4,8,9,10)(11,13)(12,15)(14,17)(16,18);(3,6,7,5)(4,8,9,10)(15,18)

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, 16551);