Finite Group DatabasebetaFinite Group Databasebeta| order | 10810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊AGL(1,𝔽47) |
| unambiguous semidirect product | D235⋊C23 |
| unambiguous semidirect product | (C47⋊C23)⋊D5 |
| Fitting, socle, derived, Hall | C5×C47 ⋊ C2×C23 |
| Hall | C5×C47⋊C23 ⋊ C2 |
| Hall | C47⋊C23 ⋊ D5 |
| Hall | D235 ⋊ C23 |
| Sylow | C47 ⋊ D5×C23 |
| Sylow | C5 ⋊ AGL(1,𝔽47) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C47 | C2×C23 |
| LCS | G ▷ C5×C47 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,23,47|b^a=b^4,d^a=d^46,d^c=d^2597 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10810, 12);