C₂×D₃×Q₁₆ #5763

order	192
automorphism	Aut(G) = D₃×#72214076 (order 6144) · Inn(G) = D₃×D₄ · Out(G) = #2403
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×D₃×Q₁₆

Fitting	C₂×C₃×Q₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂²×Q₁₆

258 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1322);