C₃²×#4020 #13087799

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

648 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 3 generators on 19 points:

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

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

maximal subgroup of	C₃²×D₅×#127, C₃⋊D₃×#4020, #72231592
maximal normal subgroup of	C₃²×D₅×#127, C₃⋊D₃×#4020, #72231592

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4116);