Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D17×C17⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (C17×D17)⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (ΓL(1,𝔽8)×D17)⋊D17 |
| unambiguous semidirect product | (D17×D119)⋊C3 |
| Fitting, socle, derived, Hall | C7×C172 ⋊ C22×C3 |
| Hall | D17×D119 ⋊ C3 |
| Hall | C172×ΓL(1,𝔽8) ⋊ C22 |
| Sylow | C172 ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ D172 |
| Sylow | C7 ⋊ C3×D172 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C172 | C22×C3 |
| LCS | G ▷ C7×C172 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 238 |
470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 78);