Finite Group DatabasebetaFinite Group Databasebeta| order | 5150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D515 |
| unambiguous semidirect product | C103⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C103 ⋊ C2 |
| Sylow | C103 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C103 | C2 |
| LCS | G ▷ C52×C103 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,103|b^a=b^4,c^a=c^4,d^a=d^1021289 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊(C5⋊(D103⋊C3)), #29508988, #29508990, … |
| maximal normal subgroup of | C5⋊(C5⋊(D103⋊C3)), #29508988, #29508990, … |
| maximal quotient of | C3⋊(C5⋊D515), C3×C5⋊D515, C7×C5⋊D515, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5150, 10);