C₁₁×#2215 #13065053

order	1408
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ G

174 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

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

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 31 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(17,21)(18,22)(19,25)(23,31)(24,29)(26,30)(27,28);(16,17,22,28,19,23,26,29,20,24,30,31,25,27,18,21);(13,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 947);