C₅×#63894 #13087151

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃²×C₅ ⋊ C₄×D₄
Sylow	C₃² ⋊ C₄×C₅×D₄

430 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 240

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 3468);