Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C31⋊#1043) |
| unambiguous semidirect product | C31⋊(C3⋊#1043) |
| Fitting, socle, derived, Hall | C3×C52×C31 ⋊ C4 |
| Hall | C52×C31 ⋊ Dic3 |
| Hall | C3×C31 ⋊ #1043 |
| Hall | C3×C52 ⋊ Dic31 |
| Sylow | C31 ⋊ C3⋊#1043 |
| Sylow | C52 ⋊ Dic93 |
| Sylow | C3 ⋊ C31⋊#1043 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C31 | C4 |
| LCS | G ▷ C3×C52×C31 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,31|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^30,d^b=d^4,e^b=e^4654 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 185);