Finite Group DatabasebetaFinite Group Databasebeta| order | 18172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D77⋊D59 |
| unambiguous semidirect product | D413⋊D11 |
| unambiguous semidirect product | D649⋊D7 |
| Fitting, socle, derived, Hall | C7×C11×C59 ⋊ C22 |
| Hall | C11×C59 ⋊ C2×D7 |
| Hall | C7×C59 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ C2×D59 |
| Sylow | C59 ⋊ D7×D11 |
| Sylow | C11 ⋊ D7×D59 |
| Sylow | C7 ⋊ D11×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C59 | C22 |
| LCS | G ▷ C7×C11×C59 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4543 |
Polycyclic presentation:
2^2,7,11,59|d^a=d^10,e^a=e^58,c^b=c^6,d^b=d^101195 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18172, 16);