Finite Group DatabasebetaFinite Group Databasebeta| order | 26666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C199 · Schur multiplier (H2) = C1 |
| direct product | D67×C199 |
| unambiguous semidirect product | C67⋊(C2×C199) |
| Fitting, socle, Hall | C67×C199 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C199 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C199 | D67 |
| commutator, cosocle, hypocenter | C67 | C2×C199 |
| Frattini | C1 | G |
| Fitting, socle | C67×C199 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C199 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13333 |
6965 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26666, 1);