PΓL(2,𝔽₉) #13089524

order	1440
isoclinism	isoclinic class of PΓL(2,𝔽₉)
automorphism	Aut(G) = PΓL(2,𝔽₉) (order 1440) · Inn(G) = G · Out(G) = C₁
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

projective general semilinear	PΓL(2,𝔽₉)
unambiguous semidirect product	S₆⋊C₂
unambiguous semidirect product	PGL(2,𝔽₉)⋊C₂
unambiguous semidirect product	#10624296⋊C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, cosocle, hypocenter	A₆	C₂²
LCS	G ▷ A₆
UCS	C₁

65 conjugacy classes of subgroups.

minimal degree	μ(G) = 10
transitive degree	μ_t(G) = 10

A minimal faithful permutation representation — 2 generators on 10 points:

(1,10,6,4,5,9,2,7,3,8);(1,10,6,4)(2,7,8,5)

maximal quotient of	#72224455
automorphism group of	A₆, SL(2,𝔽₉), S₆, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5841);