Finite Group DatabasebetaFinite Group Databasebeta| order | 24820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#13091732 |
| Fitting, socle, Hall | C5×C17×C73 ⋊ C4 |
| derived, Hall | C5×C73 ⋊ C4×C17 |
| Hall | C17×C73 ⋊ AGL(1,𝔽5) |
| Hall | C5×C17 ⋊ #64408 |
| Sylow | C73 ⋊ C17×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C17×#64408 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #13091732 |
| commutator, hypocenter | C5×C73 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C73 | C4 |
| prime radical | C17×D365 | C2 |
| cosocle | D365 | C2×C17 |
| LCS | G ▷ C5×C73 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6205 |
1615 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24820, 18);