C₁₁×#12192 #14589385

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12148
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#12192

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₁
prime radical	C₁₁×#2021	C₂
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₁₁ ◁ C₂×C₁₁×C₂²⋊C₄ ◁ G

544 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 352

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

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

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5180);