Finite Group DatabasebetaFinite Group Databasebeta| order | 26852 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D49×D137 |
| unambiguous semidirect product | (D49×C137)⋊C2 |
| unambiguous semidirect product | (C49×D137)⋊C2 |
| unambiguous semidirect product | D6713⋊C2 |
| Fitting, derived, Hall | C49×C137 ⋊ C22 |
| Sylow | C137 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×D137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C137 | C22 |
| Frattini | C7 | D7×D137 |
| socle | C7×C137 | C2×D7 |
| LCS | G ▷ C49×C137 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6713 |
1820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26852, 8);