C₂×#627 #3809

order	144
isoclinism	isoclinic class of #625
automorphism	Aut(G) = #72241543 (order 2304) · Inn(G) = D₃² · Out(G) = B(4,𝔽₂)
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

C₃² ⋊ C₂×Q₈

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 48

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 152);