Finite Group DatabasebetaFinite Group Databasebeta| order | 29388 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #28412806⋊C2 |
| unambiguous semidirect product | #28412810⋊C2 |
| unambiguous semidirect product | #28412814⋊C2 |
| Fitting, socle, derived, Hall | C31×C79 ⋊ C22×C3 |
| Hall | D31×D79 ⋊ C3 |
| Hall | #20301166 ⋊ C22 |
| Sylow | C79 ⋊ C2×D31⋊C3 |
| Sylow | C31 ⋊ C2×D79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C79 | C22×C3 |
| LCS | G ▷ C31×C79 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2449 |
Polycyclic presentation:
2^2,3,31,79|e^a=e^78,d^b=d^30,d^c=d^5,e^c=e^55243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29388, 27);