Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 518400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C5 |
| abelian | C22×C52×C9×C31 |
| multiplicative | (ℤ/30701)ˣ, (ℤ/61402)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C3×C52×C31 |
| socle, prime radical | C22×C3×C52×C31 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
240 conjugacy classes of subgroups.
27900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 216);