Finite Group DatabasebetaFinite Group Databasebeta| order | 30401 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×C43⋊C7 |
| unambiguous semidirect product | C43⋊(C7×C101) |
| unambiguous semidirect product | (C43×C101)⋊C7 |
| Fitting, socle, Hall | C43×C101 ⋊ C7 |
| derived, Sylow | C43 ⋊ C7×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | C43⋊C7 |
| commutator, cosocle, hypocenter | C43 | C7×C101 |
| Frattini | C1 | G |
| Fitting, socle | C43×C101 | C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C101 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4343 |
1313 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30401, 1);