Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C31 ⋊ C3×C4 |
| Hall | C31⋊#1043 ⋊ C3 |
| Hall | C31×C52⋊C3 ⋊ C4 |
| Hall | C52⋊C3 ⋊ Dic31 |
| Sylow | C31 ⋊ #1043⋊C3 |
| Sylow | C52 ⋊ C3×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C31 | C3×C4 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5^2,31|a^2=c,d^a=d^3,e^a=e^3,f^a=f^30,d^b=d^3e^3,e^b=d^4e,d^c=d^4,e^c=e^4164 conjugacy classes — view the full character table.
| maximal subgroup of | (C31⋊C3)⋊(#1043⋊C3), C3×#22604863, C3⋊#22604863 |
| maximal normal subgroup of | (C31⋊C3)⋊(#1043⋊C3), C3×#22604863 |
| maximal quotient of | #42124510, C3×#22604863, C3⋊#22604863 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 137);