C₃×#87642 #11924229

order	1176
isoclinism	isoclinic class of #87640
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₇² ⋊ Q₈
Sylow	C₇² ⋊ C₃×Q₈

66 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 2 generators on 25 points:

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

maximal subgroup of	C₃×#11716101, D₃×#87642, #72246620, …
maximal normal subgroup of	C₃×#11716101, D₃×#87642, #72246620, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 144);