Finite Group DatabasebetaFinite Group Databasebeta| order | 10370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D61⋊C5 |
| unambiguous semidirect product | D61⋊(C5×C17) |
| unambiguous semidirect product | (C61⋊C5)⋊(C2×C17) |
| unambiguous semidirect product | (C17×D61)⋊C5 |
| Fitting, socle, Hall | C17×C61 ⋊ C2×C5 |
| derived, Sylow | C61 ⋊ C2×C5×C17 |
| Hall | C17×C61⋊C5 ⋊ C2 |
| Hall | C17×D61 ⋊ C5 |
| Hall | C61⋊C5 ⋊ C2×C17 |
| Hall | D61 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D61⋊C5 |
| commutator, cosocle, hypocenter | C61 | C2×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C61 | C2×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | C17×#6923⋊C5, #16861898⋊C5, D17×D61⋊C5, … |
| maximal normal subgroup of | C17×#6923⋊C5, #16861898⋊C5, D17×D61⋊C5, … |
| maximal quotient of | C17×Dic61⋊C5, C2×C17×D61⋊C5, C3×C17×D61⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10370, 10);