Finite Group DatabasebetaFinite Group Databasebeta| order | 17170 |
| isoclinism | isoclinic class of C101⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C2×C17×C101⋊C5 |
| unambiguous semidirect product | (C2×C101)⋊(C5×C17) |
| unambiguous semidirect product | (C2×C17×C101)⋊C5 |
| Fitting, socle, Hall | C2×C17×C101 ⋊ C5 |
| derived, Sylow | C101 ⋊ C2×C5×C17 |
| Hall | C17×C101 ⋊ C2×C5 |
| Hall | C2×C101 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | C101⋊C5 |
| commutator, cosocle, hypocenter | C101 | C2×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C101 | C5 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C2×C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3434 |
850 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C17×C101⋊C5, C17×Dic101⋊C5, Dic17×C101⋊C5, … |
| maximal normal subgroup of | C4×C17×C101⋊C5, C17×Dic101⋊C5, Dic17×C101⋊C5, … |
| maximal quotient of | C4×C17×C101⋊C5, C22×C17×C101⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17170, 2);