C₉×C₄⋊#168 #13083765

order	1440
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₉×C₄⋊#168
unambiguous semidirect product	C₄⋊(C₉×#168)

Hall	C₅×C₉ ⋊ C₄⋊C₈
Sylow	C₅ ⋊ C₉×C₄⋊C₈

114 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1440

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

(1,2,3,4,5,6,7,8,9)(10,11,13,14,12)(15,16,17,18);(11,12)(13,14)(16,18)(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, 82);