C₂×C₄²⋊C₉ #63423

order	288
isoclinism	isoclinic class of C₄²⋊C₃
automorphism	Aut(G) = C₃×#4626⋊C₂ (order 1152) · Inn(G) = C₄²⋊C₃ · Out(G) = C₃×D₄
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₄

Aliases

direct product	C₂×C₄²⋊C₉
unambiguous semidirect product	(C₂×C₄²)⋊C₉

derived	C₄² ⋊ C₂×C₉
Sylow	C₂×C₄² ⋊ C₉

50 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 71);