Finite Group DatabasebetaFinite Group Databasebeta| order | 34602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×D79⋊C3 |
| unambiguous semidirect product | D79⋊(C3×C73) |
| unambiguous semidirect product | (C79⋊C3)⋊(C2×C73) |
| Fitting, socle, Hall | C73×C79 ⋊ C2×C3 |
| derived, Sylow | C79 ⋊ C2×C3×C73 |
| Hall | C73×C79⋊C3 ⋊ C2 |
| Hall | C73×D79 ⋊ C3 |
| Hall | C79⋊C3 ⋊ C2×C73 |
| Hall | D79 ⋊ C3×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | D79⋊C3 |
| commutator, cosocle, hypocenter | C79 | C2×C3×C73 |
| Frattini | C1 | G |
| Fitting, socle | C73×C79 | C2×C3 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C73 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5767 |
1387 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34602, 13);