Finite Group DatabasebetaFinite Group Databasebeta| order | 24444 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽7)×D291 |
| unambiguous semidirect product | D7⋊(C3×D291) |
| unambiguous semidirect product | (C3×AGL(1,𝔽7))⋊D97 |
| unambiguous semidirect product | (AGL(1,𝔽7)×C97)⋊D3 |
| Fitting, socle, derived | C3×C7×C97 ⋊ C22×C3 |
| Hall | C3×ΓL(1,𝔽8)×C97 ⋊ C22 |
| Hall | C7×C97 ⋊ C2×C3×D3 |
| Sylow | C97 ⋊ D3×AGL(1,𝔽7) |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D97 |
| Sylow | C7 ⋊ C2×C3×D291 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C97 | C22×C3 |
| LCS | G ▷ C3×C7×C97 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2037 |
1029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24444, 161);