C₂×C₃₁×AGL(1,ℤ/8) #14520754

order	1984
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₃₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

298 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.

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

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 496

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(3,4)(5,7)(6,8)(9,10);(4,7)(5,10)(8,9);(4,8)(7,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 254);