C₂×C₁₉×#2021 #18029400

order	4864
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁸

Aliases

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

3986 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 608

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 16429);