Finite Group DatabasebetaFinite Group Databasebeta| order | 12580 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C17×#3866 |
| Fitting, socle, Hall | C5×C17×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C4×C5×C17 |
| Hall | C17×C37 ⋊ C4×C5 |
| Hall | C5×C37 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | #3866 |
| commutator, hypocenter | C37 | C4×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C37 | C4 |
| prime radical | C5×C17×D37 | C2 |
| cosocle | D37 | C2×C5×C17 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C5×C17 | |
24 conjugacy classes of subgroups.
1105 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C17×#3866⋊C3, C3×C5×C17×#3866, C5×C17×C3⋊#3866 |
| maximal normal subgroup of | C5×C17×#3866⋊C3, C3×C5×C17×#3866 |
| maximal quotient of | C3×C5×C17×#3866, C5×C17×C3⋊#3866 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12580, 10);