Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| unambiguous semidirect product | D75⋊(C11⋊D11) |
| Fitting, derived, Hall | C3×C112×C25 ⋊ C22 |
| Hall | C112×C25 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D25 |
| Sylow | C112 ⋊ D3×D25 |
| Hall | C3×C25 ⋊ C2×C11⋊D11 |
| Sylow | C25 ⋊ D3×C11⋊D11 |
| Sylow | C3 ⋊ D25×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C112×C25 | C22 |
| Frattini | C5 | D15⋊(C11⋊D11) |
| socle | C3×C5×C112 | C2×D5 |
| LCS | G ▷ C3×C112×C25 | |
| UCS | C1 | |
420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9075 |
Polycyclic presentation:
2^2,3,5,11^2,5|d^5=g^4,d^a=d^4g,e^a=e^10,f^a=f^10,g^a=g^4,c^b=c^2,d^b=d^4g,g^b=g^42382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 328);