Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C5⋊((C11⋊D11)⋊C9) |
| unambiguous semidirect product | (C5⋊(C11⋊D11))⋊C9 |
| derived, Hall | C5×C112 ⋊ C2×C9 |
| Hall | C5×C112⋊C9 ⋊ C2 |
| Hall | C5⋊(C11⋊D11) ⋊ C9 |
| Hall | C112⋊C9 ⋊ D5 |
| Sylow | C112 ⋊ C9×D5 |
| Sylow | C5 ⋊ (C11⋊D11)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊((C11⋊D11)⋊C3) |
| commutator, hypocenter | C5×C112 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C112 | C2×C3 |
| prime radical | C3×C5⋊(C11⋊D11) | C3 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,11^2,3|b^3=f,c^a=c^4,d^a=d^10,e^a=e^10,d^b=d^7e^5,e^b=d^4e^3336 conjugacy classes — view the full character table.
| maximal subgroup of | #36344869, #14559097⋊C9, #14546095⋊D5, … |
| maximal normal subgroup of | #36344869, #14559097⋊C9, #14546095⋊D5, … |
| maximal quotient of | (C11⋊Dic55)⋊C9, C2×C5⋊((C11⋊D11)⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 64);