D₉×D₁₁ #87673

order	396
isoclinism	isoclinic class of D₉×D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₉×D₁₁
unambiguous semidirect product	(C₁₁×D₉)⋊C₂
unambiguous semidirect product	(C₉×D₁₁)⋊C₂
unambiguous semidirect product	D₉₉⋊C₂

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁	C₂²
Frattini	C₃	D₃×D₁₁
socle	C₃×C₁₁	C₂×D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 99

A minimal faithful permutation representation — 2 generators on 20 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,17,15,14,19,16,18,13,20);(1,2,4,6,8,10,11,9,7,5,3)(13,15)(14,18)(16,19)(17,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(396, 5);