Finite Group DatabasebetaFinite Group Databasebeta| order | 29748 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C37×C67 ⋊ C3×C4 |
| Hall | C37×Dic67 ⋊ C3 |
| Hall | #21418334 ⋊ C4 |
| Hall | Dic67 ⋊ C37⋊C3 |
| Sylow | C67 ⋊ C4×C37⋊C3 |
| Sylow | C37 ⋊ (C67⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #28415605 |
| commutator, hypocenter | C37×C67 | C3×C4 |
| Fitting, socle, cosocle | C2×C37×C67 | C2×C3 |
| prime radical | C2×#21418334 | C2 |
| LCS | G ▷ C37×C67 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9916 |
Polycyclic presentation:
2,3,37,67,2|a^2=e,d^a=d^66,c^b=c^26,d^b=d^37874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29748, 15);