C₅×#63389 #13083832

order	1440
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₅×C₉ ⋊ C₂²⋊C₈
Sylow	C₉ ⋊ C₅×C₂²⋊C₈

150 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

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

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 149);