Finite Group DatabasebetaFinite Group Databasebeta| order | 26979 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×C232⋊C3 |
| unambiguous semidirect product | C232⋊(C3×C17) |
| unambiguous semidirect product | (C17×C232)⋊C3 |
| Fitting, socle, Hall | C17×C232 ⋊ C3 |
| derived, Sylow | C232 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C232⋊C3 |
| commutator, cosocle, hypocenter | C232 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C232 | C3 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1173 |
3043 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26979, 3);