C₂×#41⋊C₉ #63699

order	288
isoclinism	isoclinic class of SL(2,𝔽₃)
automorphism	Aut(G) = C₃×D₄×S₄ (order 576) · Inn(G) = A₄ · Out(G) = C₂×C₃×D₄
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×#41⋊C₉
unambiguous semidirect product	(C₂×#41)⋊C₉

85 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2)(3,7,11,5,10,6,8,4,9)(12,13,16,19)(14,18,22,25,15,24,21,27,20,17,23,26);(1,2)(12,20,16,22)(13,24,19,26)(14,23,21,15)(17,27,25,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 347);