C₁₁×#19084 #14596277

order	2816
nilpotency class	3
isoclinism	isoclinic class of #19072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#19084

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

824 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 230 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) = 43
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,22)(14,23,26,27)(15,25,19,24)(16,21,17,20)(28,29,34,31)(30,38,41,43)(32,37,33,36)(35,42,39,40);(12,14)(13,19)(15,22)(16,24)(17,25)(18,26)(20,27)(21,23)(28,30,34,41)(29,35,31,39)(32,40,33,42)(36,38,37,43);(12,15,18,19)(13,14,22,26)(16,27,17,23)(20,25,21,24)(28,31,34,29)(30,39,41,35)(32,36,33,37)(38,42,43,40);(12,16,18,17)(13,20,22,21)(14,24,26,25)(15,23,19,27)(28,32,34,33)(29,36,31,37)(30,40,41,42)(35,38,39,43)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 12072);