Finite Group DatabasebetaFinite Group Databasebeta| order | 31758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C67×C79 ⋊ C2×C3 |
| Hall | #30629542 ⋊ C2 |
| Hall | C67×D79 ⋊ C3 |
| Hall | D79 ⋊ C67⋊C3 |
| Sylow | C79 ⋊ C2×C67⋊C3 |
| Sylow | C67 ⋊ D79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C67×C79 | C2×C3 |
| LCS | G ▷ C67×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5293 |
Polycyclic presentation:
2,3,67,79|d^a=d^78,c^b=c^37,d^b=d^23921 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31758, 15);