C₁₁×#7831 #14585024

order	2816
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁×#7831

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

350 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 2816

A minimal faithful permutation representation — 3 generators on 51 points:

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

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, 819);