C₁₁×#13056 #14590249

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2202
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13056

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	B(4,𝔽₂)
commutator	C₂×Q₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×Q₈	C₂³×C₁₁
prime radical	C₂×C₁₁×2₋¹⁺⁴	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₁₁ ◁ C₂²×Q₈×C₁₁ ◁ G

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

normal subgroups only

This group has 632 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) = 47
transitive degree	μ_t(G) = 704

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

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6044);