C₁₁×#2679 #13065517

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

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

1000 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 224 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)(12,13,14,15)(16,17,18,19);(13,15)(21,23);(16,17)(18,19)(20,21)(22,23);(12,13)(14,15)(16,17)(18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1411);