Finite Group DatabasebetaFinite Group Databasebeta| order | 8300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C83⋊#1044 |
| Fitting, socle, derived, Hall | C52×C83 ⋊ C4 |
| Sylow | C83 ⋊ #1044 |
| Sylow | C52 ⋊ Dic83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C83 | C4 |
| LCS | G ▷ C52×C83 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,83|a^2=b,c^a=c^2,d^a=d^3,e^a=e^82,c^b=c^4,d^b=d^4584 conjugacy classes — view the full character table.
| maximal subgroup of | C83⋊#64480, C3×C83⋊#1044, C3⋊(C83⋊#1044) |
| maximal normal subgroup of | C3×C83⋊#1044 |
| maximal quotient of | C3×C83⋊#1044, C3⋊(C83⋊#1044) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8300, 25);