Finite Group DatabasebetaFinite Group Databasebeta| order | 23821 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C41 · Schur multiplier (H2) = C1 |
| direct product | C7×C83⋊C41 |
| unambiguous semidirect product | C83⋊(C7×C41) |
| unambiguous semidirect product | (C7×C83)⋊C41 |
| Fitting, socle, Hall | C7×C83 ⋊ C41 |
| derived, Sylow | C83 ⋊ C7×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C83⋊C41 |
| commutator, cosocle, hypocenter | C83 | C7×C41 |
| Frattini | C1 | G |
| Fitting, socle | C7×C83 | C41 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 581 |
301 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23821, 1);