#35527

order	256
nilpotency class	2
isoclinism	isoclinic class of #35346
automorphism	Aut(G) order 1048576
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹×C₄

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

3071 conjugacy classes of subgroups; only the 575 normal subgroups are shown.

normal subgroups only

This group has 3071 conjugacy classes of subgroups — too many to draw. Only its 575 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 64

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

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 28515);