Finite Group DatabasebetaFinite Group Databasebeta| order | 27856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D1741 |
| unambiguous semidirect product | C23⋊D1741 |
| Fitting | C23×C1741 ⋊ C2 |
| Sylow | C1741 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D1741 |
| commutator, cosocle | C2×C1741 | C23 |
| Frattini | C2 | C22×D1741 |
| Fitting | C23×C1741 | C2 |
| socle | C22×C1741 | C22 |
| hypercenter | C23 | D1741 |
| hypocenter | C1741 | C2×D4 |
| LCS | G ▷ C2×C1741 ▷ C1741 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13928 |
6970 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27856, 35);