C₅×#63837 #13087184

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃²×C₅ ⋊ C₄×Q₈
Sylow	C₃² ⋊ C₄×C₅×Q₈

306 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 23 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 3501);