Finite Group DatabasebetaFinite Group Databasebeta| order | 10270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D79⋊C13) |
| unambiguous semidirect product | D395⋊C13 |
| unambiguous semidirect product | (C79⋊C13)⋊D5 |
| Fitting, socle, derived, Hall | C5×C79 ⋊ C2×C13 |
| Hall | C5×C79⋊C13 ⋊ C2 |
| Hall | C79⋊C13 ⋊ D5 |
| Hall | D395 ⋊ C13 |
| Sylow | C79 ⋊ D5×C13 |
| Sylow | C5 ⋊ D79⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C79 | C2×C13 |
| LCS | G ▷ C5×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,13,79|b^a=b^4,d^a=d^78,d^c=d^1867 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10270, 12);