C₂×C₁₁×#537 #13066286

order	1408
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₁ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×C₁₁×#537

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

1640 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 704

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 2180);