Finite Group DatabasebetaFinite Group Databasebeta| order | 10100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C101⋊C5 |
| unambiguous semidirect product | (Dic5×C101)⋊C5 |
| derived | C5×C101 ⋊ C4×C5 |
| Hall | C5×C101⋊C5 ⋊ C4 |
| Sylow | C101 ⋊ C5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×C101⋊C5 |
| commutator, hypocenter | C5×C101 | C4×C5 |
| Fitting, socle, cosocle | C2×C5×C101 | C2×C5 |
| prime radical | C2×C5×C101⋊C5 | C2 |
| LCS | G ▷ C5×C101 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
200 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic5×C101⋊C5, Dic15×C101⋊C5 |
| maximal normal subgroup of | C3×Dic5×C101⋊C5 |
| maximal quotient of | C3×Dic5×C101⋊C5, Dic15×C101⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10100, 26);