Finite Group DatabasebetaFinite Group Databasebeta| order | 10100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic505⋊C5 |
| derived | C5×C101 ⋊ C4×C5 |
| Hall | C5×C101⋊C5 ⋊ C4 |
| Sylow | C101 ⋊ C5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(D101⋊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.
Polycyclic presentation:
2,5^2,101,2|a^2=e,c^a=c^4,d^a=d^100,d^b=d^95140 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic505⋊C5, C3⋊(Dic505⋊C5) |
| maximal normal subgroup of | C3×Dic505⋊C5 |
| maximal quotient of | C3×Dic505⋊C5, C3⋊(Dic505⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10100, 25);