Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×C3×C5×C11 ⋊ C2 |
| Hall | C3×C5×C11 ⋊ D4 |
| Hall | C5×C11 ⋊ #67 |
| Hall | C3×C11 ⋊ C22⋊D5 |
| Hall | C3×C5 ⋊ C22⋊D11 |
| Sylow | C11 ⋊ #1220 |
| Sylow | C5 ⋊ #63159 |
| Sylow | C3 ⋊ C22⋊D55 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D165 |
| commutator, socle, cosocle | C2×C3×C5×C11 | C22 |
| Fitting | C22×C3×C5×C11 | C2 |
| hypercenter | C22 | D165 |
| hypocenter | C3×C5×C11 | D4 |
| LCS | G ▷ C2×C3×C5×C11 ▷ C3×C5×C11 | |
| UCS | C1 ◁ C2 ◁ C22 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 660 |
Polycyclic presentation:
2^3,3,5,11|b^a=bc,d^a=d^2,e^a=e^4,f^a=f^10333 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 129);