C₁₁×#11573 #14588766

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11549
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#11573

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₁
prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

358 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 106 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)(12,13,16,20,17,21,15,19)(14,18,22,25,23,26,24,27)(28,29,31,35,32,36,39,43)(30,33,37,41,38,34,40,42);(12,14)(13,18)(15,24)(16,22)(17,23)(19,27)(20,25)(21,26)(29,33,36,34)(31,39)(35,41,43,42)(37,40);(12,15,17,16)(13,19,21,20)(14,22,23,24)(18,25,26,27)

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, 4561);