C₁₁×#10936 #14588129

order	2816
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₁×#10936

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	#120
commutator	C₂³	C₂×C₄²×C₁₁
Frattini, cosocle	C₂⁵	C₂³×C₁₁
prime radical	C₂⁵×C₁₁	C₂³
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂⁵×C₁₁ ◁ G

1258 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 302 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) = 704

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

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

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3924);