C₃⋊#95 #831

order	96
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = D₃×#2846 (order 768) · Inn(G) = C₂×D₃ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

C₃ ⋊ #95

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 15 points:

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

Polycyclic presentation:

2^5,3|a^2=c,b^2=d,b^a=be,f^a=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 38);