Finite Group DatabasebetaFinite Group Databasebeta| order | 8300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C83⋊#1035 |
| Fitting, derived, Hall | C25×C83 ⋊ C4 |
| Sylow | C83 ⋊ #1035 |
| Sylow | C25 ⋊ Dic83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C83 | C4 |
| Frattini | C5 | C83⋊AGL(1,𝔽5) |
| socle | C5×C83 | AGL(1,𝔽5) |
| LCS | G ▷ C25×C83 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,83,5|a^2=b,c^5=e,c^a=c^2e,d^a=d^82,e^a=e^2,c^b=c^4e^4,e^b=e^4584 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C83⋊#1035, C3⋊(C83⋊#1035) |
| maximal normal subgroup of | C3×C83⋊#1035 |
| maximal quotient of | C3×C83⋊#1035, C3⋊(C83⋊#1035) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8300, 7);