C₇×#216 #66619

order	336
isoclinism	isoclinic class of #213
automorphism	Aut(G) = C₂²×C₃×D₃×D₄ (order 576) · Inn(G) = #67 · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₇ ⋊ Q₁₆
Sylow	C₃ ⋊ C₇×Q₁₆

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3)(4,14,8,6)(5,18,11,9)(7,13,17,16)(10,12,15,19)(20,21,22,23,24,25,26);(2,3)(4,11,8,5)(6,19,14,12)(7,10,17,15)(9,13,18,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 88);