Finite Group DatabasebetaFinite Group Databasebeta| order | 17918 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C17⋊D527 |
| unambiguous semidirect product | C31⋊(C17⋊D17) |
| Fitting, socle, derived, Hall | C172×C31 ⋊ C2 |
| Sylow | C172 ⋊ D31 |
| Sylow | C31 ⋊ C17⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C172×C31 | C2 |
| LCS | G ▷ C172×C31 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8959 |
Polycyclic presentation:
2,17^2,31|b^a=b^16,c^a=c^16,d^a=d^304481 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×D527, D31×C17⋊D17, C2×C17⋊D527 |
| maximal normal subgroup of | D17×D527, D31×C17⋊D17, C2×C17⋊D527 |
| maximal quotient of | C31⋊#11923880, C2×C17⋊D527 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17918, 6);