C₁₁×#2537 #13065375

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

788 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 704

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1269);