Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C3)⋊#1042 |
| unambiguous semidirect product | (C31⋊#1042)⋊C3 |
| Fitting, socle, derived, Hall | C52×C31 ⋊ C3×C4 |
| Hall | C31⋊#1042 ⋊ C3 |
| Hall | C52×C31⋊C3 ⋊ C4 |
| Hall | C31⋊C3 ⋊ #1042 |
| Sylow | C31 ⋊ C3×#1042 |
| 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 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5^2,31|a^2=c,d^a=d^2,e^a=e^4,f^a=f^30,f^b=f^5,d^c=d^4139 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C31⋊C3)⋊#1042, C3⋊((C31⋊C3)⋊#1042) |
| maximal normal subgroup of | C3×(C31⋊C3)⋊#1042 |
| maximal quotient of | (C31⋊C9)⋊#1042, C3×(C31⋊C3)⋊#1042, C3⋊((C31⋊C3)⋊#1042) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 124);