Finite Group DatabasebetaFinite Group Databasebeta| order | 10452 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#19104944 |
| Fitting, socle | C2×C13×C67 ⋊ C2×C3 |
| derived, Hall | C13×C67 ⋊ C22×C3 |
| Hall | C2×C13×D67 ⋊ C3 |
| Hall | #14579731 ⋊ C22 |
| Hall | C2×D67 ⋊ C13⋊C3 |
| Sylow | C67 ⋊ C22×C13⋊C3 |
| Sylow | C13 ⋊ C2×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19104944 |
| commutator, cosocle, hypocenter | C13×C67 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C67 | C2×C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
314 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13⋊C3×D67⋊C3, D3×#19104944, C2×C3×#19104944, … |
| maximal normal subgroup of | C2×C13⋊C3×D67⋊C3, C2×C3×#19104944 |
| maximal quotient of | C2×#30627894, D3×#19104944, C2×C3×#19104944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10452, 45);