C₁₁×#19080 #14596273

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

Aliases

direct product

C₁₁×#19080

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#3548	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 936 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) = 1408

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)(28,29,33,37)(30,38,40,43)(31,36,32,35)(34,41,42,39);(12,13,17,21)(14,19,24,27)(15,20,16,18)(22,26,23,25)(28,30,33,40)(29,34,37,42)(31,39,32,41)(35,38,36,43);(12,14)(13,19)(15,22)(16,23)(17,24)(18,25)(20,26)(21,27)(31,32)(35,36)(38,43)(39,41);(12,15,17,16)(13,20,21,18)(14,23,24,22)(19,25,27,26)(28,31,33,32)(29,35,37,36)(30,39,40,41)(34,38,42,43)

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, 12068);