Finite Group DatabasebetaFinite Group Databasebeta| order | 11580 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16838804⋊C3 |
| Fitting, socle, derived, Hall | C5×C193 ⋊ C3×C4 |
| Hall | #16838804 ⋊ C3 |
| Hall | C5×C193⋊C3 ⋊ C4 |
| Hall | C193⋊C3 ⋊ Dic5 |
| Sylow | C193 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ #11715871⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C193 | C3×C4 |
| prime radical | C5×D193⋊C3 | C2 |
| cosocle | C5×D193 | C2×C3 |
| LCS | G ▷ C5×C193 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,193|a^2=c,d^a=d^4,e^a=e^81,e^b=e^84,e^c=e^192104 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16838804⋊C3, C3⋊(#16838804⋊C3) |
| maximal normal subgroup of | C3×#16838804⋊C3 |
| maximal quotient of | #16838804⋊C9, C3×#16838804⋊C3, C3⋊(#16838804⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11580, 19);