Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C3)⋊#1035 |
| unambiguous semidirect product | (C31⋊#1035)⋊C3 |
| Fitting, derived, Hall | C25×C31 ⋊ C3×C4 |
| Hall | C31⋊#1035 ⋊ C3 |
| Hall | C25×C31⋊C3 ⋊ C4 |
| Hall | C31⋊C3 ⋊ #1035 |
| Sylow | C31 ⋊ C3×#1035 |
| Sylow | C25 ⋊ (C31⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C31 | C3×C4 |
| Frattini | C5 | (C31⋊C3)⋊AGL(1,𝔽5) |
| socle | C5×C31 | C3×AGL(1,𝔽5) |
| LCS | G ▷ C25×C31 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,31,5|a^2=c,d^5=f,d^a=d^2f,e^a=e^30,f^a=f^2,e^b=e^5,d^c=d^4f^4,f^c=f^4100 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C31⋊C3)⋊#1035, C3⋊((C31⋊C3)⋊#1035) |
| maximal normal subgroup of | C3×(C31⋊C3)⋊#1035 |
| maximal quotient of | (C31⋊C9)⋊#1035, C3×(C31⋊C3)⋊#1035, C3⋊((C31⋊C3)⋊#1035) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 26);