C₂×C₁₉×#394 #14560243

order	2432
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁷

Aliases

C₂×C₁₉×#394

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

1252 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 33 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1118);