C₉⋊A₄ #1092

order	108
isoclinism	isoclinic class of C₉⋊A₄
automorphism	Aut(G) = C₃×D₃×A₄ (order 216) · Inn(G) = C₃×A₄ · Out(G) = C₂×C₃
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₂

Aliases

C₉⋊A₄

Fitting	C₂²×C₉ ⋊ C₃
Sylow	C₂² ⋊ 3₋¹⁺²

19 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 13 points:

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

Polycyclic presentation:

3^3,2^2|b^3=c,b^a=bc,d^a=e,e^a=de

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(108, 19);