C₅×C₄⋊(C₉⋊C₈) #13083806

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

Aliases

direct product	C₅×C₄⋊(C₉⋊C₈)
unambiguous semidirect product	C₄⋊(C₅×C₉⋊C₈)

Hall	C₅×C₉ ⋊ C₄⋊C₈
Sylow	C₉ ⋊ C₅×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)(6,11,13,12,7,9,8,14,10)(15,16,17,18);(7,9)(8,12)(10,11)(13,14)(16,18)(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, 123);