Finite Group DatabasebetaFinite Group Databasebeta| order | 10100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×Dic101⋊C5 |
| unambiguous semidirect product | Dic101⋊C52 |
| unambiguous semidirect product | (C5×Dic101)⋊C5 |
| derived, Sylow | C101 ⋊ C4×C52 |
| Hall | C5×C101⋊C5 ⋊ C4 |
| Hall | Dic101 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D101⋊C5 |
| commutator, hypocenter | C101 | C4×C52 |
| Frattini | C2 | C5×D101⋊C5 |
| Fitting, socle | C2×C5×C101 | C2×C5 |
| prime radical | C2×C5×C101⋊C5 | C2 |
| cosocle | C2×C101 | C2×C52 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C2×C5 | |
48 conjugacy classes of subgroups.
200 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×Dic101⋊C5, C5×C3⋊(Dic101⋊C5) |
| maximal normal subgroup of | C3×C5×Dic101⋊C5 |
| maximal quotient of | C3×C5×Dic101⋊C5, C5×C3⋊(Dic101⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10100, 24);