C₂²×C₁₁×C₂²⋊Q₈ #13066271

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

Aliases

C₂²×C₁₁×C₂²⋊Q₈

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

1840 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 5 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 2165);