Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊D575 |
| Fitting, derived, Hall | C32×C23×C25 ⋊ C22 |
| Hall | C23×C25 ⋊ D32 |
| Hall | C32×C25 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×D25 |
| Sylow | C25 ⋊ (C3⋊D3)⋊D23 |
| Sylow | C23 ⋊ (C3⋊D3)⋊D25 |
| Sylow | C32 ⋊ C2×D575 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C23×C25 | C22 |
| Frattini | C5 | (C3⋊D3)⋊D115 |
| socle | C32×C5×C23 | C2×D5 |
| LCS | G ▷ C32×C23×C25 | |
| UCS | C1 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3450 |
Polycyclic presentation:
2^2,3^2,5,23,5|e^5=g^4,d^a=d^2,e^a=e^4g,f^a=f^22,g^a=g^4,c^b=c^2,d^b=d^21731 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 88);