Finite Group DatabasebetaFinite Group Databasebeta| order | 578 |
| isoclinism | isoclinic class of C17⋊D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C17⋊D17 |
| Fitting, socle, derived, Sylow | C172 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C172 | C2 |
| LCS | G ▷ C172 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 289 |
Polycyclic presentation:
2,17^2|b^a=b^16,c^a=c^16146 conjugacy classes — view the full character table.
| maximal subgroup of | #11923883, #11923884, D172, … |
| maximal normal subgroup of | #11923883, #11923884, D172, … |
| maximal quotient of | #11923880, C2×C17⋊D17, C3⋊(C17⋊D17), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(578, 4);