C₁₁×#547 #10623408

order	704
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₁₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ G

292 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.

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

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 4 generators on 23 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,20,21)(18,19,22,23);(17,21)(19,23);(12,13)(14,15)(16,18,20,22)(17,19,21,23);(16,19)(17,22)(18,21)(20,23)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(704, 1327);