Finite Group DatabasebetaFinite Group Databasebeta| order | 24514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(D103⋊C17) |
| unambiguous semidirect product | D721⋊C17 |
| unambiguous semidirect product | (C103⋊C17)⋊D7 |
| Fitting, socle, derived, Hall | C7×C103 ⋊ C2×C17 |
| Hall | C7×C103⋊C17 ⋊ C2 |
| Hall | C103⋊C17 ⋊ D7 |
| Hall | D721 ⋊ C17 |
| Sylow | C103 ⋊ D7×C17 |
| Sylow | C7 ⋊ D103⋊C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C103 | C2×C17 |
| LCS | G ▷ C7×C103 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 721 |
Polycyclic presentation:
2,7,17,103|b^a=b^6,d^a=d^102,d^c=d^72106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24514, 12);