Finite Group DatabasebetaFinite Group Databasebeta| order | 34602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C73×C79 ⋊ C2×C3 |
| Hall | #31772448 ⋊ C2 |
| Hall | C73×D79 ⋊ C3 |
| Hall | D79 ⋊ C73⋊C3 |
| Sylow | C79 ⋊ C2×C73⋊C3 |
| Sylow | C73 ⋊ D79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C73×C79 | C2×C3 |
| LCS | G ▷ C73×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5767 |
Polycyclic presentation:
2,3,73,79|d^a=d^78,c^b=c^8,d^b=d^551003 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34602, 16);