Finite Group DatabasebetaFinite Group Databasebeta| order | 26740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic191⋊C5 |
| unambiguous semidirect product | Dic191⋊(C5×C7) |
| unambiguous semidirect product | (C191⋊C5)⋊(C4×C7) |
| unambiguous semidirect product | (C7×Dic191)⋊C5 |
| derived, Sylow | C191 ⋊ C4×C5×C7 |
| Hall | C7×C191⋊C5 ⋊ C4 |
| Hall | C7×Dic191 ⋊ C5 |
| Hall | C7×C191 ⋊ C4×C5 |
| Hall | C191⋊C5 ⋊ C4×C7 |
| Hall | Dic191 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D191⋊C5 |
| commutator, hypocenter | C191 | C4×C5×C7 |
| Frattini | C2 | C7×D191⋊C5 |
| Fitting, socle | C2×C7×C191 | C2×C5 |
| prime radical | C2×C7×C191⋊C5 | C2 |
| cosocle | C2×C191 | C2×C5×C7 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5348 |
406 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26740, 10);