Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | D29×C5⋊D45 |
| unambiguous semidirect product | (C5×D29)⋊D45 |
| unambiguous semidirect product | (C9×D29)⋊(C5⋊D5) |
| Fitting, derived, Hall | C52×C9×C29 ⋊ C22 |
| Hall | C52×C29 ⋊ C2×D9 |
| Hall | C9×C29 ⋊ C2×C5⋊D5 |
| Hall | C52×C9 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C5⋊D45 |
| Sylow | C52 ⋊ D9×D29 |
| Sylow | C9 ⋊ C5⋊D5×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9×C29 | C22 |
| Frattini | C3 | D29×C3⋊(C5⋊D5) |
| socle | C3×C52×C29 | C2×D3 |
| LCS | G ▷ C52×C9×C29 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6525 |
1824 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 199);