#17102

order	256
nilpotency class	2
isoclinism	isoclinic class of #17082
automorphism	Aut(G) order 1310720
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵×C₄²

Aliases

No aliases for this group.

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂⁴	C₂⁴
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ G
LECS	G ▷ C₂⁴ ▷ C₁

1483 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 16 points:

(2,4)(6,8)(9,10,11,12)(13,14,15,16);(5,6,7,8)(9,10)(11,12)(13,14,15,16);(6,8)(10,12)(13,14)(15,16);(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)

Polycyclic presentation:

2^8|a^2=f,b^2=ef,b^a=be,c^a=cf,d^a=dh,c^b=cg,d^b=def,d^c=de

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 10090);