Finite Group DatabasebetaFinite Group Databasebeta| order | 26718 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C61×C73 ⋊ C2×C3 |
| Hall | #27211344 ⋊ C2 |
| Hall | C73×D61 ⋊ C3 |
| Hall | D61 ⋊ C73⋊C3 |
| Sylow | C73 ⋊ D61⋊C3 |
| Sylow | C61 ⋊ C2×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C61×C73 | C2×C3 |
| LCS | G ▷ C61×C73 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4453 |
Polycyclic presentation:
2,3,61,73|c^a=c^60,c^b=c^47,d^b=d^8784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26718, 19);