C₂×C₁₉×#120 #11926197

order	1216
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁷

Aliases

C₂×C₁₉×#120

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

662 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 4 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1216, 202);