Finite Group DatabasebetaFinite Group Databasebeta| order | 24900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D249 |
| unambiguous semidirect product | (C3×D5)⋊(C5×D83) |
| unambiguous semidirect product | (D5×C83)⋊(C5×D3) |
| Fitting, socle, Hall | C3×C52×C83 ⋊ C22 |
| derived | C3×C5×C83 ⋊ C22×C5 |
| Hall | C52×C83 ⋊ C2×D3 |
| Hall | C3×C83 ⋊ C2×C5×D5 |
| Sylow | C83 ⋊ C5×D3×D5 |
| Hall | C3×C52 ⋊ C2×D83 |
| Sylow | C52 ⋊ C2×D249 |
| Sylow | C3 ⋊ C5×D5×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D249 |
| commutator, cosocle, hypocenter | C3×C5×C83 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C83 | C22 |
| LCS | G ▷ C3×C5×C83 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2490 |
2520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24900, 78);