#34981

order	256
nilpotency class	2
isoclinism	isoclinic class of #34980
automorphism	Aut(G) order 524288
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

No aliases for this group.

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

2563 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 5 generators on 16 points:

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

Polycyclic presentation:

2^8|b^2=f,b^a=bf,c^a=cg,e^a=eh,c^b=ch,d^b=dh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27969);