C₁₁×#23805 #14600998

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23391
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#23805

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄³×C₁₁ ◁ G

974 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 974 conjugacy classes of subgroups — too many to draw. Only its 286 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) = 39
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11)(16,17,19,20)(18,21,22,23)(24,25,28,33,30,32,29,34)(26,35,36,39,27,38,37,31);(12,13)(14,15)(17,20)(21,23)(24,26,30,27)(25,31,32,39)(28,37,29,36)(33,38,34,35);(13,15)(24,27,30,26)(25,31,32,39)(28,36,29,37)(33,38,34,35);(16,18,19,22)(17,21,20,23)(25,32)(31,39)(33,34)(35,38)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16793);