Finite Group DatabasebetaFinite Group Databasebeta| order | 24444 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)⋊#87604) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3⋊#87604) |
| Fitting, socle, derived | C3×C7×C97 ⋊ C3×C4 |
| Hall | C3×ΓL(1,𝔽8)×C97 ⋊ C4 |
| Hall | C7×C97 ⋊ C3×Dic3 |
| Sylow | C97 ⋊ C3⋊(ΓL(1,𝔽8)⋊C4) |
| Hall | C3×ΓL(1,𝔽8) ⋊ #87604 |
| Sylow | C7 ⋊ C3×C3⋊#87604 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C97 | C3×C4 |
| prime radical | C3×ΓL(1,𝔽8)×D97 | C2 |
| cosocle | C3×C7×D97 | C2×C3 |
| LCS | G ▷ C3×C7×C97 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2037 |
Polycyclic presentation:
2,3,2,3,7,97|a^2=c,d^a=d^2,e^a=e^6,f^a=f^75,e^b=e^2,f^c=f^96384 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24444, 150);