C₂×Q₈×C₁₁² #14515563

order	1936
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁² · Schur multiplier (H₂) = C₂²×C₁₁

Aliases

C₂×Q₈×C₁₁²

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁²	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₁₁²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁² ◁ G

266 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 1936

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2)(11,12,13,14,15,16,17,18,19,20,21);(3,4,5,6)(7,10,9,8)(22,23,24,25,26,27,28,29,30,31,32);(3,7,5,9)(4,8,6,10)

1210 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1936, 157);