Finite Group DatabasebetaFinite Group Databasebeta| order | 33418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D2387 |
| unambiguous semidirect product | C11⋊(C7⋊D217) |
| unambiguous semidirect product | C31⋊(C7⋊D77) |
| Fitting, socle, derived, Hall | C72×C11×C31 ⋊ C2 |
| Hall | C72×C31 ⋊ D11 |
| Hall | C72×C11 ⋊ D31 |
| Hall | C11×C31 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D341 |
| Sylow | C31 ⋊ C7⋊D77 |
| Sylow | C11 ⋊ C7⋊D217 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C11×C31 | C2 |
| LCS | G ▷ C72×C11×C31 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16709 |
Polycyclic presentation:
2,7^2,11,31|b^a=b^6,c^a=c^6,d^a=d^10,e^a=e^308356 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33418, 20);