C₁₁×#2313 #13065151

order	1408
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₁ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₁×#2313

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₁
Frattini, cosocle	C₂³	C₂⁴×C₁₁
prime radical	C₂⁴×C₁₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

512 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 704

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

484 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14647241, #14647302, #14647312, …
maximal subgroup of	C₁₁×#8737, C₁₁×#8755, C₁₁×#8758, …
maximal normal subgroup of	C₁₁×#8737, C₁₁×#8755, C₁₁×#8758, …
maximal quotient of	C₁₁×#13776, C₁₁×#13778, C₁₁×#13787, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1045);