Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×ΓL(1,𝔽8)⋊#595 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C17×#595) |
| unambiguous semidirect product | (C7⋊#595)⋊(C3×C17) |
| unambiguous semidirect product | (C17×C7⋊#595)⋊C3 |
| Fitting, socle, Hall | C7×C172 ⋊ C3×C4 |
| derived | C7×C17 ⋊ C3×C4×C17 |
| Hall | C17×C7⋊#595 ⋊ C3 |
| Hall | C172×ΓL(1,𝔽8) ⋊ C4 |
| Sylow | C172 ⋊ ΓL(1,𝔽8)⋊C4 |
| Hall | ΓL(1,𝔽8) ⋊ C17×#595 |
| Sylow | C7 ⋊ C3×C17×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | ΓL(1,𝔽8)⋊#595 |
| commutator, hypocenter | C7×C17 | C3×C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C172 | C3×C4 |
| prime radical | C17×ΓL(1,𝔽8)×D17 | C2 |
| cosocle | C7×D17 | C2×C3×C17 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 476 |
578 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 76);