C₁₁×#13342 #14590535

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13342

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₁₁×#3150	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

558 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 122 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)(16,17,24,31)(18,26,36,46)(19,37,32,25)(20,28,40,47)(21,27,38,41)(22,30,23,29)(33,44,39,43)(34,45,35,42);(12,13)(14,15)(16,18)(17,25)(19,38)(20,39)(21,32)(22,35)(23,34)(24,36)(26,28)(27,45)(29,44)(30,43)(31,37)(33,40)(41,42)(46,47);(13,15)(16,19)(17,26)(18,20)(21,34)(22,33)(23,39)(24,32)(25,41)(27,37)(28,44)(29,45)(30,42)(31,46)(35,38)(36,40)(43,47)

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, 6330);