Finite Group DatabasebetaFinite Group Databasebeta| order | 8300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊D5)⋊D83 |
| unambiguous semidirect product | D415⋊D5 |
| Fitting, socle, derived, Hall | C52×C83 ⋊ C22 |
| Sylow | C83 ⋊ D52 |
| Sylow | C52 ⋊ C2×D83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C83 | C22 |
| LCS | G ▷ C52×C83 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,83|c^a=c^4,e^a=e^82,c^b=c^4,d^b=d^4590 conjugacy classes — view the full character table.
| maximal subgroup of | ((C5⋊D5)⋊C3)⋊D83, C3×(C5⋊D5)⋊D83, D415⋊D15, … |
| maximal normal subgroup of | C3×(C5⋊D5)⋊D83 |
| maximal quotient of | C3×(C5⋊D5)⋊D83, D415⋊D15, #38735281 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8300, 31);