Finite Group DatabasebetaFinite Group Databasebeta| order | 16660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | C7⋊D7×D85 |
| Fitting, socle, derived, Hall | C5×C72×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D17 |
| Hall | C5×C17 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×D85 |
| Sylow | C17 ⋊ D5×C7⋊D7 |
| Sylow | C5 ⋊ D17×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C17 | C22 |
| LCS | G ▷ C5×C72×C17 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4165 |
1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16660, 87);