C₁₁×#19077 #14596270

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

Aliases

direct product

C₁₁×#19077

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#3151	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 996 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) = 35
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 4 generators on 35 points:

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

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, 12065);