Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊D775 |
| Fitting, derived, Hall | C32×C25×C31 ⋊ C22 |
| Hall | C25×C31 ⋊ D32 |
| Hall | C32×C31 ⋊ C2×D25 |
| Hall | C32×C25 ⋊ C2×D31 |
| Sylow | C31 ⋊ (C3⋊D3)⋊D25 |
| Sylow | C25 ⋊ (C3⋊D3)⋊D31 |
| Sylow | C32 ⋊ C2×D775 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C25×C31 | C22 |
| Frattini | C5 | (C3⋊D3)⋊D155 |
| socle | C32×C5×C31 | C2×D5 |
| LCS | G ▷ C32×C25×C31 | |
| UCS | C1 | |
132 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,31,5|e^5=g^4,d^a=d^2,e^a=e^4g,f^a=f^30,g^a=g^4,c^b=c^2,d^b=d^22331 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 195);