Finite Group DatabasebetaFinite Group Databasebeta| order | 26908 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D312 |
| unambiguous semidirect product | (C31×D31)⋊(C2×C7) |
| unambiguous semidirect product | (C31⋊D31)⋊(C2×C7) |
| Fitting, socle, Hall | C7×C312 ⋊ C22 |
| derived, Sylow | C312 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D312 |
| commutator, cosocle, hypocenter | C312 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C312 | C22 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C7 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 434 |
2023 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26908, 18);