Finite Group DatabasebetaFinite Group Databasebeta| order | 30682 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C23⋊D667 |
| unambiguous semidirect product | C29⋊(C23⋊D23) |
| Fitting, socle, derived, Hall | C232×C29 ⋊ C2 |
| Sylow | C232 ⋊ D29 |
| Sylow | C29 ⋊ C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C232×C29 | C2 |
| LCS | G ▷ C232×C29 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15341 |
Polycyclic presentation:
2,23^2,29|b^a=b^22,c^a=c^22,d^a=d^287672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30682, 10);