Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C17 |
| direct product | AGL(1,𝔽7)×C17⋊D17 |
| unambiguous semidirect product | D7⋊(C3×C17⋊D17) |
| unambiguous semidirect product | (C17×AGL(1,𝔽7))⋊D17 |
| Fitting, socle, derived, Hall | C7×C172 ⋊ C22×C3 |
| Hall | D7×C17⋊D17 ⋊ C3 |
| Hall | C172×ΓL(1,𝔽8) ⋊ C22 |
| Sylow | C172 ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C2×C17⋊D17 |
| Sylow | C7 ⋊ C2×C3×C17⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C172 | C22×C3 |
| LCS | G ▷ C7×C172 | |
| UCS | C1 | |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2023 |
1022 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 80);