Finite Group DatabasebetaFinite Group Databasebeta| order | 10524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16812881 |
| Fitting, socle, Hall | C3×C877 ⋊ C4 |
| derived, Sylow | C877 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16812881 |
| commutator, hypocenter | C877 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C877 | C4 |
| prime radical | C3×D877 | C2 |
| cosocle | D877 | C2×C3 |
| LCS | G ▷ C877 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
669 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10524, 10);