Finite Group DatabasebetaFinite Group Databasebeta| order | 10580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D115⋊D23 |
| unambiguous semidirect product | (C23⋊D23)⋊D5 |
| Fitting, socle, derived, Hall | C5×C232 ⋊ C22 |
| Sylow | C232 ⋊ C2×D5 |
| Sylow | C5 ⋊ D232 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C232 | C22 |
| LCS | G ▷ C5×C232 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,23^2|c^a=c^4,d^a=d^22,d^b=d^22,e^b=e^22701 conjugacy classes — view the full character table.
| maximal subgroup of | ((C23⋊D23)⋊C3)⋊D5, C3×D115⋊D23, #44540752, … |
| maximal normal subgroup of | C3×D115⋊D23 |
| maximal quotient of | C3×D115⋊D23, #44540752, D115⋊D69 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10580, 28);