C₁₁×#13616 #14590809

order	2816
nilpotency class	5
isoclinism	isoclinic class of #2263
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#13616

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×D₁₆
commutator	C₁₆	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₁
prime radical	C₂×C₁₁×#508	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ C₂²×C₁₁×C₁₆ ◁ G

302 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 47
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(17,22)(18,26)(19,28)(20,32)(23,35)(24,38)(25,39)(27,31)(29,45)(30,42)(33,44)(34,36)(37,46)(40,41)(43,47);(16,17)(18,27)(19,31)(20,34)(21,23)(22,26)(24,28)(25,32)(29,46)(30,43)(33,47)(35,42)(36,45)(37,44)(38,40)(39,41);(17,23)(22,35)(24,37)(25,34)(27,43)(31,47)(36,39)(38,46)

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, 6604);