C₃³×Dic₁₃ #13064036

order	1404
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₃³×C₄ · Schur multiplier (H₂) = C₃³

Aliases

C₃³×Dic₁₃

derived, Sylow	C₁₃ ⋊ C₃³×C₄
Hall	C₃³×C₁₃ ⋊ C₄

168 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1404

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3)(10,11)(12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26);(4,5,6)(10,12,11,13)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21);(7,8,9)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 168);