Finite Group DatabasebetaFinite Group Databasebeta| order | 10100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14523088⋊C5 |
| Fitting, socle, derived | C5×C101 ⋊ C4×C5 |
| Hall | C5×C101⋊C5 ⋊ C4 |
| Sylow | C101 ⋊ C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C101 | C4×C5 |
| prime radical | C5⋊(D101⋊C5) | C2 |
| cosocle | D505 | C2×C5 |
| LCS | G ▷ C5×C101 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,5,101|a^2=c,d^a=d^2,e^a=e^91,e^b=e^95,d^c=d^4,e^c=e^10050 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#14523088⋊C5, C3⋊(#14523088⋊C5) |
| maximal normal subgroup of | C3×#14523088⋊C5 |
| maximal quotient of | C3×#14523088⋊C5, C3⋊(#14523088⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10100, 39);