Finite Group DatabasebetaFinite Group Databasebeta| order | 10778 |
| automorphism | Aut(G) order 27246784 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5389 |
| unambiguous semidirect product | C17⋊D317 |
| unambiguous semidirect product | C317⋊D17 |
| Fitting, socle, derived, Hall | C17×C317 ⋊ C2 |
| Sylow | C317 ⋊ D17 |
| Sylow | C17 ⋊ D317 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C317 | C2 |
| LCS | G ▷ C17×C317 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,317|b^a=b^16,c^a=c^3162696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36340685, #36340686, D17×D317, … |
| maximal normal subgroup of | #36340685, #36340686, D17×D317, … |
| maximal quotient of | Dic5389, C2×D5389, C3×D5389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10778, 3);