Finite Group DatabasebetaFinite Group Databasebeta| order | 16762 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C172 · Schur multiplier (H2) = C17 |
| direct product | C172×D29 |
| unambiguous semidirect product | C29⋊(C2×C172) |
| Fitting, socle, Hall | C172×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C172 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C172 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C172 |
| Frattini | C1 | G |
| Fitting, socle | C172×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C172 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8381 |
4624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C172×#1181, C17×#14520310, C17×D17×D29, … |
| maximal normal subgroup of | C172×#1181, C17×#14520310, C17×D17×D29, … |
| maximal quotient of | C172×Dic29, C2×C172×D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16762, 10);