C₅×#63728 #13085556

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃²×C₅ ⋊ #101
Sylow	C₃² ⋊ C₅×#101

134 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

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

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3,4,5)(6,8)(7,10,11)(12,14,15,22,16,21,24,27)(13,17,18,25,19,20,23,26);(6,7)(8,11)(9,10)(12,13,16,19)(14,20,21,17)(15,23,24,18)(22,25,27,26)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1873);