Finite Group DatabasebetaFinite Group Databasebeta| order | 26668 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D59×D113 |
| unambiguous semidirect product | (C113×D59)⋊C2 |
| unambiguous semidirect product | (C59×D113)⋊C2 |
| unambiguous semidirect product | D6667⋊C2 |
| Fitting, socle, derived, Hall | C59×C113 ⋊ C22 |
| Sylow | C113 ⋊ C2×D59 |
| Sylow | C59 ⋊ C2×D113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C59×C113 | C22 |
| LCS | G ▷ C59×C113 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6667 |
1798 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26668, 8);