Finite Group DatabasebetaFinite Group Databasebeta| order | 17170 |
| isoclinism | isoclinic class of D101 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C17×D101 |
| Fitting, socle, Hall | C5×C17×C101 ⋊ C2 |
| derived, Sylow | C101 ⋊ C2×C5×C17 |
| Hall | C17×C101 ⋊ C2×C5 |
| Hall | C5×C101 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | D101 |
| commutator, cosocle, hypocenter | C101 | C2×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C101 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C5×C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8585 |
4420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C17×#87938, C5×#20293557, C5×D17×D101, … |
| maximal normal subgroup of | C5×C17×#87938, C5×#20293557, C5×D17×D101, … |
| maximal quotient of | C5×C17×Dic101, C2×C5×C17×D101 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17170, 3);