C₂²×C₃⋊D₉ #6275

order	216
isoclinism	isoclinic class of C₃⋊D₉
automorphism	Aut(G) order 69984
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂²×C₃⋊D₉

Fitting	C₂²×C₃×C₉ ⋊ C₂
derived, Sylow	C₃×C₉ ⋊ C₂³

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂³
Frattini	C₃	C₂²×C₃⋊D₃
Fitting	C₂²×C₃×C₉	C₂
socle	C₂²×C₃²	D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂²

160 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(216, 112);