C₃×#87648 #11924274

order	1176
isoclinism	isoclinic class of #87648
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₇

Aliases

Hall	C₃×C₇² ⋊ Q₈
Sylow	C₇² ⋊ C₃×Q₈

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1176

A minimal faithful permutation representation — 3 generators on 25 points:

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

303 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 189);