C₂²×AΣL(1,𝔽₁₆) #33341

order	256
nilpotency class	4
isoclinism	isoclinic class of AΣL(1,𝔽₁₆)
automorphism	Aut(G) order 49152
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1387 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1387 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.

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

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 4 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26329);