C₁₁×#19056 #14596249

order	2816
nilpotency class	3
isoclinism	isoclinic class of #19050
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₁×#19056

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#3549	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

992 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 992 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 704

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

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 12044);