Finite Group DatabasebetaFinite Group Databasebeta| order | 29748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #28415606⋊C2 |
| unambiguous semidirect product | #28415610⋊C2 |
| unambiguous semidirect product | #28415614⋊C2 |
| Fitting, socle, derived, Hall | C37×C67 ⋊ C22×C3 |
| Hall | D37×D67 ⋊ C3 |
| Hall | #21418335 ⋊ C22 |
| Sylow | C67 ⋊ C2×D37⋊C3 |
| Sylow | C37 ⋊ C2×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C67 | C22×C3 |
| LCS | G ▷ C37×C67 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2479 |
Polycyclic presentation:
2^2,3,37,67|e^a=e^66,d^b=d^36,d^c=d^26,e^c=e^29244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29748, 32);