Q₈²×C₁₃ #11719593

order	832
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

Q₈²×C₁₃

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

212 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 4 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1559);