Finite Group DatabasebetaFinite Group Databasebeta| order | 3332 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D49 |
| unambiguous semidirect product | (C17×D49)⋊C2 |
| unambiguous semidirect product | (D17×C49)⋊C2 |
| unambiguous semidirect product | D833⋊C2 |
| Fitting, derived, Hall | C17×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C17×C49 | C22 |
| Frattini | C7 | D7×D17 |
| socle | C7×C17 | C2×D7 |
| LCS | G ▷ C17×C49 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 66 |
| transitive degree | μt(G) = 833 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D17×D49, D17×D245, D49×D85, … |
| maximal normal subgroup of | C5×D17×D49, C11×D17×D49 |
| maximal quotient of | C5×D17×D49, D17×D245, D49×D85, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3332, 8);