C₁₁×#1984 #13064822

order	1408
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#1984

Subgroups

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

292 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1408

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

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

Conjugacy classes & character table

616 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14640398, #14640585, #14640777, …
maximal subgroup of	C₁₁×#7057, C₁₁×#7128, C₁₁×#7206, …
maximal normal subgroup of	C₁₁×#7057, C₁₁×#7128, C₁₁×#7206, …
maximal quotient of	C₁₁×#9864, C₁₁×#9865, C₁₁×#9866, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 716);