Finite Group DatabasebetaFinite Group Databasebeta| order | 21900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#20300469 |
| Fitting, derived, Hall | C3×C25×C73 ⋊ C4 |
| Hall | C25×C73 ⋊ Dic3 |
| Hall | C3×C73 ⋊ #1035 |
| Hall | C3×C25 ⋊ #64408 |
| Sylow | C73 ⋊ C3⋊#1035 |
| Sylow | C25 ⋊ C3⋊#64408 |
| Sylow | C3 ⋊ #20300469 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C25×C73 | C4 |
| Frattini | C5 | C3⋊#13091732 |
| socle | C3×C5×C73 | AGL(1,𝔽5) |
| prime radical, cosocle | C3×D1825 | C2 |
| LCS | G ▷ C3×C25×C73 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5475 |
Polycyclic presentation:
2^2,3,5,73,5|a^2=b,d^5=f,c^a=c^2,d^a=d^2f,e^a=e^27,f^a=f^2,d^b=d^4f^4,e^b=e^72,f^b=f^41374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21900, 34);