Finite Group DatabasebetaFinite Group Databasebeta| order | 25996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D67×D97 |
| unambiguous semidirect product | (C97×D67)⋊C2 |
| unambiguous semidirect product | (C67×D97)⋊C2 |
| unambiguous semidirect product | D6499⋊C2 |
| Fitting, socle, derived, Hall | C67×C97 ⋊ C22 |
| Sylow | C97 ⋊ C2×D67 |
| Sylow | C67 ⋊ C2×D97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C67×C97 | C22 |
| LCS | G ▷ C67×C97 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6499 |
1750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25996, 8);