#13794

order	256
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	Aut(G) order 6291456
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, socle, cosocle	C₂⁴	C₂⁴
commutator	C₂²	C₂²×C₄²
prime radical	C₂⁶	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ G
LECS	G ▷ C₂⁴ ▷ C₁

2231 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 20 points:

(6,8)(9,10,12,11)(13,14)(15,17)(16,19)(18,20);(14,15)(18,19);(1,2,3,4)(5,6,7,8)(9,11,12,10)(13,15,17,14)(16,19,20,18);(13,16)(14,18)(15,19)(17,20)

Polycyclic presentation:

2^8|a^2=g,c^2=h,b^a=be,c^a=cf,d^a=de,c^b=ce

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6782);