Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C11⋊D11)⋊C3)⋊D17 |
| Fitting, socle, Hall | C112×C17 ⋊ C2×D3 |
| derived, Hall | C17×C112⋊C3 ⋊ C22 |
| Hall | C112⋊C3 ⋊ C2×D17 |
| Sylow | C112 ⋊ C2×D51 |
| Sylow | C17 ⋊ #10624391⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C17×C112⋊C3 | C22 |
| Fitting, socle | C112×C17 | C2×D3 |
| LCS | G ▷ C17×C112⋊C3 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 561 |
Polycyclic presentation:
2^2,3,17,11^2|c^a=c^2,d^a=d^16,e^a=e^3f^10,f^a=e^8f^8,e^b=e^10,f^b=f^10,e^c=e^2f^10,f^c=e^7f^8239 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 50);