C₅×C₉⋊#95 #13083833

order	1440
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₅×C₉⋊#95
unambiguous semidirect product	C₉⋊(C₅×#95)

Hall	C₅×C₉ ⋊ #95
Sylow	C₉ ⋊ C₅×#95

228 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 128 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) = 1440

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

(1,2,3,4,5)(6,11,13,12,7,9,8,14,10)(19,20,21,22)(24,26);(7,9)(8,12)(10,11)(13,14)(15,16,17,18)(23,24)(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, 150);