C₁₁×#12298 #14589491

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12298
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle	C₂×C₁₁	#1613
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
prime radical	C₁₁×#3192	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×M₁₆ ◁ G

376 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 176

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5286);