C₂⁴×D₉ #64191

order	288
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product	C₂⁴×D₉
unambiguous semidirect product	C₉⋊C₂⁵
unambiguous semidirect product	(C₂×C₉)⋊C₂⁴

Fitting	C₂⁴×C₉ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂⁵

	subgroup	G/H
center, hypercenter	C₂⁴	D₉
commutator, cosocle, hypocenter	C₉	C₂⁵
Frattini	C₃	C₂⁴×D₃
Fitting	C₂⁴×C₉	C₂
socle	C₂⁴×C₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂⁴

1122 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 5 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 839);