Finite Group DatabasebetaFinite Group Databasebeta| order | 24414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D313⋊C3)⋊C13 |
| unambiguous semidirect product | (D313⋊C13)⋊C3 |
| unambiguous semidirect product | ((C313⋊C3)⋊C13)⋊C2 |
| Fitting, socle, derived, Sylow | C313 ⋊ C2×C3×C13 |
| Hall | (C313⋊C3)⋊C13 ⋊ C2 |
| Hall | D313⋊C13 ⋊ C3 |
| Hall | C313⋊C13 ⋊ C2×C3 |
| Hall | D313⋊C3 ⋊ C13 |
| Hall | C313⋊C3 ⋊ C2×C13 |
| Hall | D313 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C313 | C2×C3×C13 |
| LCS | G ▷ C313 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 313 |
Polycyclic presentation:
2,3,13,313|d^a=d^312,d^b=d^214,d^c=d^10382 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24414, 30);