Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #6057 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | C3×#87840 |
| Hall | C3×C52 ⋊ C4⋊C4 |
| Sylow | C52 ⋊ C3×C4⋊C4 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3)(4,6,12,7)(5,8,13,9)(14,15,16,17);(4,5)(6,10,11,9)(7,13,12,8)48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 619);