Q₈×C₁₁×#41 #13066316

order	1408
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₁ · Schur multiplier (H₂) = C₂⁸

Aliases

Q₈×C₁₁×#41

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂⁵
prime radical	C₂×C₁₁×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

1068 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 2210);