Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5×C11 ⋊ Q8 |
| Hall | C5×C11 ⋊ Dic6 |
| Hall | C3×C11 ⋊ Dic10 |
| Hall | C3×C5 ⋊ Dic22 |
| Sylow | C11 ⋊ #1204 |
| Sylow | C5 ⋊ #63143 |
| Sylow | C3 ⋊ Dic110 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D55 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C3×C5×C11 | C22 |
| hypocenter | C3×C5×C11 | Q8 |
| LCS | G ▷ C2×C3×C5×C11 ▷ C3×C5×C11 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1320 |
Polycyclic presentation:
2^3,3,5,11|a^2=c,b^2=c,b^a=bc,e^a=e^4,f^a=f^10,d^b=d^2171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 86);