Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C31⋊C3)⋊#1044 |
| unambiguous semidirect product | (C31⋊#1044)⋊C3 |
| Fitting, socle, derived, Hall | C52×C31 ⋊ C3×C4 |
| Hall | C31⋊#1044 ⋊ C3 |
| Hall | C52×C31⋊C3 ⋊ C4 |
| Hall | C31⋊C3 ⋊ #1044 |
| Sylow | C31 ⋊ C3×#1044 |
| Sylow | C52 ⋊ (C31⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C31 | C3×C4 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5^2,31|a^2=c,d^a=d^2,e^a=e^3,f^a=f^30,f^b=f^5,d^c=d^4,e^c=e^4100 conjugacy classes — view the full character table.
| maximal subgroup of | (C31⋊C3)⋊#64480, C3×(C31⋊C3)⋊#1044, C3⋊((C31⋊C3)⋊#1044) |
| maximal normal subgroup of | C3×(C31⋊C3)⋊#1044 |
| maximal quotient of | (C31⋊C9)⋊#1044, C3×(C31⋊C3)⋊#1044, C3⋊((C31⋊C3)⋊#1044) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 122);