C₁₁×#9514 #14586707

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#9514

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

478 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 704

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2502);