Finite Group DatabasebetaFinite Group Databasebeta| order | 29388 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C3)⋊Dic79 |
| derived, Hall | C31×C79 ⋊ C3×C4 |
| Hall | Dic2449 ⋊ C3 |
| Hall | C79×C31⋊C3 ⋊ C4 |
| Hall | C31⋊C3 ⋊ Dic79 |
| Sylow | C79 ⋊ (C31⋊C3)⋊C4 |
| Sylow | C31 ⋊ C3×Dic79 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C31⋊C3)⋊D79 |
| commutator, hypocenter | C31×C79 | C3×C4 |
| Fitting, socle, cosocle | C2×C31×C79 | C2×C3 |
| prime radical | C2×C79×C31⋊C3 | C2 |
| LCS | G ▷ C31×C79 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9796 |
Polycyclic presentation:
2,3,31,79,2|a^2=e,c^a=c^30,d^a=d^78,c^b=c^251036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29388, 22);