Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊#11923876 |
| unambiguous semidirect product | (C7⋊#11923876)⋊C3 |
| Fitting, derived, Hall | C7×C289 ⋊ C3×C4 |
| Hall | C7⋊#11923876 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C289 ⋊ C4 |
| Sylow | C289 ⋊ ΓL(1,𝔽8)⋊C4 |
| Hall | ΓL(1,𝔽8) ⋊ #11923876 |
| Sylow | C7 ⋊ C3×#11923876 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C289 | C3×C4 |
| Frattini | C17 | ΓL(1,𝔽8)⋊#595 |
| socle | C7×C17 | C3×#595 |
| prime radical | ΓL(1,𝔽8)×D289 | C2 |
| cosocle | C7×D289 | C2×C3 |
| LCS | G ▷ C7×C289 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2023 |
Polycyclic presentation:
2,3,2,7,17^2|a^2=c,e^17=f^11,d^a=d^6,e^a=e^13f,f^a=f^13,d^b=d^4,e^c=e^16f^6,f^c=f^16374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 15);