C₁₁×#2014 #13064852

order	1408
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₁
prime radical	C₂×C₁₁×#127	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

474 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.

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

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(20,21,24,27)(22,25,23,26);(13,15)(16,17)(18,19)(21,25)(22,23)(26,27);(17,19)(21,26)(22,23)(25,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 746);