Finite Group DatabasebetaFinite Group Databasebeta| order | 27300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×D21⋊D13 |
| unambiguous semidirect product | D21⋊(C25×D13) |
| unambiguous semidirect product | D39⋊(D7×C25) |
| unambiguous semidirect product | D91⋊(D3×C25) |
120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6825 |
2175 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27300, 180);