Finite Group DatabasebetaFinite Group Databasebeta| order | 12005 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C49 · Schur multiplier (H2) = C72 |
| direct product | C5×C72⋊C49 |
| unambiguous semidirect product | C72⋊(C5×C49) |
| unambiguous semidirect product | (C5×C72)⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C5×C72 | C72 |
| commutator | C7 | C5×C7×C49 |
| Frattini, cosocle | C72 | C5×C72 |
| prime radical | C5×C73 | C7 |
| LCS | G ▷ C7 ▷ C1 | |
| UCS | C1 ◁ C5×C72 ◁ G | |
94 conjugacy classes of subgroups.
1925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12005, 3);