Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#5398 |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5)(6,7,9)(10,12,19,23,14,21,13,20)(11,15,22,25,17,24,16,18);(7,8)(10,11,14,17)(12,18,21,25)(13,22,19,16)(15,23,24,20)110 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#73036, C5×#73037, C5×#73134, … |
| maximal normal subgroup of | C5×#73036, C5×#73037, C5×#73134, … |
| maximal quotient of | C5×#73014, C5×#73015, C5×#73016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6264);