Finite Group DatabasebetaFinite Group Databasebeta| order | 828 |
| isoclinism | isoclinic class of D9×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D23 |
| unambiguous semidirect product | (D9×C23)⋊C2 |
| unambiguous semidirect product | (C9×D23)⋊C2 |
| unambiguous semidirect product | D207⋊C2 |
| Fitting, derived, Hall | C9×C23 ⋊ C22 |
| Sylow | C23 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C23 | C22 |
| Frattini | C3 | D3×D23 |
| socle | C3×C23 | C2×D3 |
| LCS | G ▷ C9×C23 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 207 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×D23, C5×D9×D23, D23×D45, … |
| maximal normal subgroup of | C2×D9×D23, C5×D9×D23, C17×D9×D23, … |
| maximal quotient of | #13110167, D9×Dic23, D207⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(828, 5);