Finite Group DatabasebetaFinite Group Databasebeta| order | 12005 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C5×#14558879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C5×C7 | H(3,𝔽7) |
| commutator, Frattini, cosocle | C72 | C5×C72 |
| prime radical | C5×H(3,𝔽7) | C7 |
| LCS | G ▷ C72 ▷ C7 ▷ C1 | |
| UCS | C1 ◁ C5×C7 ◁ C5×C72 ◁ G | |
44 conjugacy classes of subgroups.
485 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12005, 10);