Finite Group DatabasebetaFinite Group Databasebeta| order | 17205 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#16812215 |
| Fitting, socle, Hall | C5×C31×C37 ⋊ C3 |
| derived, Hall | C31×C37 ⋊ C3×C5 |
| Hall | C5×C37 ⋊ C31⋊C3 |
| Hall | C5×C31 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ C5×C31⋊C3 |
| Sylow | C31 ⋊ C5×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #16812215 |
| commutator, cosocle, hypocenter | C31×C37 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C37 | C3 |
| LCS | G ▷ C31×C37 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5735 |
1925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×#16812215, C5×#20293708, C5×#20293712, … |
| maximal normal subgroup of | C2×C5×#16812215, C5×#20293708, C5×#20293712, … |
| maximal quotient of | C2×C5×#16812215 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17205, 5);