Finite Group DatabasebetaFinite Group Databasebeta| order | 27508 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×D13×D23 |
| unambiguous semidirect product | (C23×D13)⋊(C2×C23) |
| unambiguous semidirect product | (C13×D23)⋊(C2×C23) |
| unambiguous semidirect product | D299⋊(C2×C23) |
| Fitting, socle, Hall | C13×C232 ⋊ C22 |
| derived | C13×C23 ⋊ C22×C23 |
| Sylow | C232 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×C23×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D13×D23 |
| commutator, cosocle, hypocenter | C13×C23 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C13×C232 | C22 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C23 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 598 |
2392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27508, 26);