C₁₁×#7185 #14584378

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1304
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7185

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#95
commutator	C₂³	C₄×C₈×C₁₁
Frattini, cosocle	C₂³×C₈	C₂²×C₁₁
socle	C₂²×C₁₁	#336
prime radical	C₂⁴×C₁₁	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

314 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 51
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18,19,16)(15,17)(20,21,23,27,24,29,34,41,25,28,35,40,36,42,47,50)(22,30,32,43,33,44,46,51,31,26,37,38,45,39,48,49);(12,14)(13,16)(15,19)(17,18)(20,22)(21,26,28,30)(23,32)(24,33)(25,31)(27,38,40,43)(29,39,42,44)(34,46)(35,37)(36,45)(41,49,50,51)(47,48)

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, 173);