C₁₁×#12114 #14589307

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12114
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂×C₁₁	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×M₁₆ ◁ G

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

normal subgroups only

This group has 474 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)(14,17)(15,24)(16,20)(18,21)(19,23)(22,25)(26,27);(13,17)(14,21)(15,23)(18,19)(20,25)(22,27)(24,26);(14,22)(21,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5102);