Finite Group DatabasebetaFinite Group Databasebeta| order | 26884 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×Dic143 |
| unambiguous semidirect product | C11⋊(C47×Dic13) |
| derived, Hall | C11×C13 ⋊ C4×C47 |
| Hall | C11×C13×C47 ⋊ C4 |
| Hall | C13×C47 ⋊ Dic11 |
| Hall | C11×C47 ⋊ Dic13 |
| Sylow | C13 ⋊ Dic11×C47 |
| Sylow | C11 ⋊ C47×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | D143 |
| commutator, hypocenter | C11×C13 | C4×C47 |
| Frattini | C2 | C47×D143 |
| Fitting, socle, prime radical | C2×C11×C13×C47 | C2 |
| cosocle | C2×C11×C13 | C2×C47 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C2×C47 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26884 |
6862 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26884, 7);