C₂×#800 #4903

order	192
isoclinism	isoclinic class of D₄₈
automorphism	Aut(G) = D₃×#10576928 (order 3072) · Inn(G) = D₂₄ · Out(G) = C₂²×#41
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂×C₃×C₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂×SD₃₂

90 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 21 points:

(3,4,5)(6,7,12,18,17,21,8,11,10,14,15,20,9,13,16,19);(1,2)(4,5)(7,11)(8,15)(9,17)(12,16)(13,20)(14,19)(18,21);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 462);