C₃³×#261 #13064063

order	1404
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₃³×C₄ · Schur multiplier (H₂) = C₃³

Aliases

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

168 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 351

A minimal faithful permutation representation — 3 generators on 22 points:

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

maximal subgroup of	C₃×C₃⋊D₃×#261, C₃²×D₃×#261, #261×C₃⋊(C₃⋊D₃), …
maximal normal subgroup of	C₃×C₃⋊D₃×#261, C₃²×D₃×#261, #261×C₃⋊(C₃⋊D₃), …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 195);