C₃×#87640 #11924227

order	1176
isoclinism	isoclinic class of #87640
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇² ⋊ D₄
Sylow	C₇² ⋊ C₃×D₄

82 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 2 generators on 21 points:

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

maximal subgroup of	C₃×#11716106, D₃×#87640, #72246472, …
maximal normal subgroup of	C₃×#11716106, D₃×#87640, #72246472, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 142);