C₃×#34288 #10652895

order	768
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

3584 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 5 generators on 19 points:

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

maximal subgroup of	C₃×C₄×#3484
maximal normal subgroup of	C₃×C₄×#3484

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 27276);