Finite Group DatabasebetaFinite Group Databasebeta| order | 2108 |
| isoclinism | isoclinic class of D17×D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D31 |
| unambiguous semidirect product | (C31×D17)⋊C2 |
| unambiguous semidirect product | (C17×D31)⋊C2 |
| unambiguous semidirect product | D527⋊C2 |
| Fitting, socle, derived, Hall | C17×C31 ⋊ C22 |
| Sylow | C31 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C31 | C22 |
| LCS | G ▷ C17×C31 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 527 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D17×D31, D31×D119, D17×D217, … |
| maximal normal subgroup of | C7×D17×D31, C11×D17×D31, C13×D17×D31, … |
| maximal quotient of | C7×D17×D31, D31×D119, D17×D217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2108, 8);