C₂×C₁₁×#525 #13066273

order	1408
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₁ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×C₁₁×#525

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₁
socle	C₂³×C₁₁	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

1880 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 5 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 2167);