C₃⋊Dic₉ #1083

order	108
isoclinism	isoclinic class of C₃⋊D₉
automorphism	Aut(G) = C₂×#72210336 (order 5832) · Inn(G) = C₃⋊D₉ · Out(G) = C₂×#272
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	C₃⋊Dic₉
unambiguous semidirect product	C₉⋊Dic₃

C₃×C₉ ⋊ C₄

30 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:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(108, 10);