C₅×#6308 #11762128

order	1080
isoclinism	isoclinic class of #6308
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₃³

Aliases

Hall	C₃³×C₅ ⋊ Q₈
Sylow	C₃³ ⋊ C₅×Q₈

336 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 1080

A minimal faithful permutation representation — 4 generators on 22 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 474);