Finite Group DatabasebetaFinite Group Databasebeta| order | 26260 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1313 |
| derived, Hall | C13×C101 ⋊ C4×C5 |
| Hall | C5×C13×C101 ⋊ C4 |
| Hall | C5×C101 ⋊ Dic13 |
| Sylow | C101 ⋊ C5×Dic13 |
| Hall | C5×C13 ⋊ Dic101 |
| Sylow | C13 ⋊ C5×Dic101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1313 |
| commutator, hypocenter | C13×C101 | C4×C5 |
| Frattini | C2 | C5×D1313 |
| Fitting, socle, prime radical | C2×C5×C13×C101 | C2 |
| cosocle | C2×C13×C101 | C2×C5 |
| LCS | G ▷ C13×C101 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26260 |
6580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26260, 5);