C₁₁×#11390 #14588583

order	2816
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₁×#11390

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	#120
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂⁵	C₂³×C₁₁
prime radical	C₂⁵×C₁₁	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂⁵×C₁₁ ◁ G

1358 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 1358 conjugacy classes of subgroups — too many to draw. Only its 270 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) = 704

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)(24,25)(26,30,31,28)(27,29);(16,17,19,21)(18,22,23,20)(24,26)(25,28)(27,31)(29,30);(13,15)(16,18,19,23)(17,20,21,22)(24,25)(26,28)(27,29)(30,31)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4378);