Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2×C5×C11 |
| unambiguous semidirect product | C22⋊(C52⋊(C112⋊C3)) |
| unambiguous semidirect product | C52⋊(C22⋊(C112⋊C3)) |
| unambiguous semidirect product | C112⋊(C22⋊(C52⋊C3)) |
| Fitting, socle, derived, Hall | C22×C52×C112 ⋊ C3 |
| Hall | C52×C112 ⋊ A4 |
| Hall | C22×C112 ⋊ C52⋊C3 |
| Sylow | C112 ⋊ C22⋊(C52⋊C3) |
| Hall | C22×C52 ⋊ C112⋊C3 |
| Sylow | C52 ⋊ C22⋊(C112⋊C3) |
| Sylow | C22 ⋊ C52⋊(C112⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C52×C112 | C3 |
| LCS | G ▷ C22×C52×C112 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
Polycyclic presentation:
3,2^2,5^2,11^2|b^a=c,c^a=bc,d^a=d^4e^2,e^a=d^2,f^a=f^5g^7,g^a=f^5g^54036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 945);