Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((C11⋊Dic11)⋊C3)⋊C25 |
| unambiguous semidirect product | #27130776⋊C3 |
| derived, Sylow | C112 ⋊ C3×C4×C25 |
| Hall | #27130776 ⋊ C3 |
| Hall | (C112⋊C3)⋊C25 ⋊ C4 |
| Hall | #15690027 ⋊ C3×C4 |
| Hall | (C11⋊Dic11)⋊C3 ⋊ C25 |
| Hall | C11⋊Dic11 ⋊ C3×C25 |
| Hall | C112⋊C3 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | ((C11⋊D11)⋊C3)⋊C5 |
| commutator, hypocenter | C112 | C3×C4×C25 |
| Fitting, socle, cosocle | C2×C5×C112 | C2×C3×C5 |
| prime radical | C2×C5×C112⋊C3 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2×C5 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3300 |
Polycyclic presentation:
2,3,5,11^2,2,5|a^2=f,c^5=g,d^a=d^10,e^a=e^10,d^b=d^3e^9,e^b=de^7,d^c=d^4,e^c=e^4340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 155);