C₉×#4018 #13084348

order	1440
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

228 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 123 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 — 3 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 665);