Finite Group DatabasebetaFinite Group Databasebeta| order | 10778 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D317 |
| unambiguous semidirect product | C317⋊(C2×C17) |
| Fitting, socle, Hall | C17×C317 ⋊ C2 |
| derived, Sylow | C317 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D317 |
| commutator, cosocle, hypocenter | C317 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C317 | C2 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×#11929639, #36340688, D17×D317, … |
| maximal normal subgroup of | C17×#11929639, #36340688, D17×D317, … |
| maximal quotient of | C17×Dic317, C2×C17×D317, C3×C17×D317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10778, 2);