C₁₁×#11394 #14588587

order	2816
nilpotency class	3
isoclinism	isoclinic class of #2032
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#11394

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#393
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂⁵	C₂³×C₁₁
prime radical	C₂⁵×C₁₁	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁵×C₁₁ ◁ G

1090 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 254 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) = 352

A minimal faithful permutation representation — 3 generators on 31 points:

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

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4382);