C₂×#213 #931

order	96
isoclinism	isoclinic class of #213
automorphism	Aut(G) = D₃×#3484 (order 768) · Inn(G) = #67 · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

Fitting	C₂×C₃×D₄ ⋊ C₂
Sylow	C₃ ⋊ C₂×D₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 138);