Finite Group DatabasebetaFinite Group Databasebeta| order | 10396 |
| automorphism | Aut(G) order 12807872 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5198 |
| direct product | C2×D2599 |
| unambiguous semidirect product | (C2×C23)⋊D113 |
| unambiguous semidirect product | (C2×C113)⋊D23 |
| Fitting, socle | C2×C23×C113 ⋊ C2 |
| derived, Hall | C23×C113 ⋊ C22 |
| Sylow | C113 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2599 |
| commutator, cosocle, hypocenter | C23×C113 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C113 | C2 |
| LCS | G ▷ C23×C113 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2602 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D2599, C2×C3×D2599, C2×D7797, … |
| maximal normal subgroup of | C2×C3×D2599, D10396 |
| maximal quotient of | D3×D2599, C2×C3×D2599, C2×D7797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10396, 9);