Finite Group DatabasebetaFinite Group Databasebeta| order | 10370 |
| isoclinism | isoclinic class of C61⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C2×C17×C61⋊C5 |
| unambiguous semidirect product | (C2×C61)⋊(C5×C17) |
| unambiguous semidirect product | (C2×C17×C61)⋊C5 |
| Fitting, socle, Hall | C2×C17×C61 ⋊ C5 |
| derived, Sylow | C61 ⋊ C2×C5×C17 |
| Hall | C17×C61 ⋊ C2×C5 |
| Hall | C2×C61 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | C61⋊C5 |
| commutator, cosocle, hypocenter | C61 | C2×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C61 | C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C17 | |
16 conjugacy classes of subgroups.
578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10370, 2);