Q₈×C₁₃×#41 #13112536

order	1664
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂⁸

Aliases

Q₈×C₁₃×#41

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

1068 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 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)(11,14)(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(1664, 2210);