C₁₁×#19006 #14596199

order	2816
nilpotency class	3
isoclinism	isoclinic class of #18992
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#19006

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 938 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)(15,21)(16,20)(17,19)(18,23)(24,27)(25,26)(28,29,32,34)(30,36,38,43)(31,39,41,35)(33,40,42,37);(12,14)(13,18)(15,25)(16,23)(17,24)(19,26)(20,27)(21,22)(28,30,32,38)(29,33,34,42)(31,40,41,37)(35,43,39,36);(12,14)(13,18)(15,23)(16,25)(17,24)(19,26)(20,22)(21,27)(31,41)(35,39)(36,43)(37,40);(13,19)(18,26)(20,21)(22,27)(29,34)(33,42)(35,39)(36,43)

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, 11994);