C₁₁×#18997 #14596190

order	2816
nilpotency class	3
isoclinism	isoclinic class of #18992
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₁×#18997

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂×C₁₁×H(3,𝔽₄)	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

1066 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 352

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

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 11985);