C₁₁×#19083 #14596276

order	2816
nilpotency class	3
isoclinism	isoclinic class of #19072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#19083

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

876 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 876 conjugacy classes of subgroups — too many to draw. Only its 230 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) = 43
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,18)(14,22)(15,16)(20,21)(23,24)(25,26)(29,34)(31,32)(35,42)(36,40)(37,38)(41,43);(12,13)(14,19)(15,20)(16,18)(17,21)(22,26)(23,25)(24,27)(28,29,33,36)(30,35,39,43)(31,34,32,40)(37,42,38,41);(12,14,17,24)(13,19,21,27)(15,22,16,23)(18,25,20,26)(28,30,33,39)(29,35,36,43)(31,38,32,37)(34,41,40,42);(12,15,17,16)(13,20,21,18)(14,23,24,22)(19,25,27,26)(28,31,33,32)(29,34,36,40)(30,37,39,38)(35,42,43,41)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 12071);