Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C52×C31 ⋊ C4×C9 |
| Hall | C52⋊(C31⋊C9) ⋊ C4 |
| Hall | C31⋊#1043 ⋊ C9 |
| Sylow | C31 ⋊ #1043⋊C9 |
| Sylow | C52 ⋊ Dic31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #22604861 |
| commutator, hypocenter | C52×C31 | C4×C9 |
| Fitting, socle | C3×C52×C31 | C3×C4 |
| prime radical, cosocle | C3×C31×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5^2,31,3|a^2=c,b^3=g,d^a=d^3,e^a=e^3,f^a=f^30,d^b=de,e^b=d^2e^3,f^b=f^25,d^c=d^4,e^c=e^4252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 255);