Finite Group DatabasebetaFinite Group Databasebeta| order | 7820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#66775 |
| Fitting, socle, derived, Hall | C5×C17×C23 ⋊ C4 |
| Hall | C17×C23 ⋊ AGL(1,𝔽5) |
| Hall | C5×C23 ⋊ #595 |
| Hall | C5×C17 ⋊ Dic23 |
| Sylow | C23 ⋊ #66775 |
| Sylow | C17 ⋊ C23⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C23⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17×C23 | C4 |
| LCS | G ▷ C5×C17×C23 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,17,23|a^2=b,c^a=c^2,d^a=d^13,e^a=e^22,c^b=c^4,d^b=d^16509 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C23⋊#66775, C3⋊(C23⋊#66775) |
| maximal normal subgroup of | C3×C23⋊#66775 |
| maximal quotient of | C3×C23⋊#66775, C3⋊(C23⋊#66775) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7820, 16);