C₅×C₂²⋊#622 #13086339

order	1440
isoclinism	isoclinic class of #3788
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product	C₅×C₂²⋊#622
unambiguous semidirect product	C₂²⋊(C₅×#622)

Hall	C₃²×C₅ ⋊ C₂²⋊C₈
Sylow	C₃² ⋊ C₅×C₂²⋊C₈

208 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

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

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2656);