Dic₃×C₂₉ #66822

order	348
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×C₄×D₃×C₇ (order 336) · Inn(G) = D₃ · Out(G) = C₂×C₄×C₇
homology	Abelianization (H₁) = C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₂₉
unambiguous semidirect product	C₃⋊(C₄×C₂₉)

derived, Sylow	C₃ ⋊ C₄×C₂₉
Hall	C₃×C₂₉ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 348

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2)(3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36);(1,3,2,4)(6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(348, 1);