C₁₁×#12454 #14589647

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12433
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁×#12454

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂×D₄×C₁₁	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈×D₄×C₁₁ ◁ G

218 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 35
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,18)(14,16,19,17)(21,25)(22,26)(23,29)(27,31)(28,35)(30,34)(32,33);(20,21,26,33,23,28,30,31,24,27,34,35,29,32,22,25);(13,16)(14,19)(17,18)(21,27)(25,31)(28,32)(33,35)

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, 5442);