C₅×#63546 #13084771

order	1440
isoclinism	isoclinic class of #63546
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃²×C₅ ⋊ D₁₆
Sylow	C₃² ⋊ C₅×D₁₆

134 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 44 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)(6,7,12,18,9,13,16,19,10,14,20,21,15,17,8,11)(23,24)(25,26,27);(7,11)(8,12)(9,15)(13,21)(14,19)(16,20)(17,18)(22,23,24)(26,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1088);