C₁₁×#2197 #13065035

order	1408
nilpotency class	4
isoclinism	isoclinic class of #2196
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂×C₁₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂³×C₁₁
prime radical	C₁₁×B(4,𝔽₂)	C₂
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₁₁ ◁ C₂×D₄×C₁₁ ◁ G

258 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 56 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)(14,20)(15,18)(16,19)(17,21)(22,26)(23,25)(24,27);(12,14,16,22)(13,17,19,24)(15,21,23,27)(18,20,25,26);(15,23)(21,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 929);