Finite Group DatabasebetaFinite Group Databasebeta| order | 3502 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D103⋊C17 |
| unambiguous semidirect product | (C103⋊C17)⋊C2 |
| Fitting, socle, derived, Sylow | C103 ⋊ C2×C17 |
| Hall | C103⋊C17 ⋊ C2 |
| Hall | D103 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C103 | C2×C17 |
| LCS | G ▷ C103 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 103 |
Polycyclic presentation:
2,17,103|c^a=c^102,c^b=c^7237 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D103⋊C17, C5⋊(D103⋊C17), C7×D103⋊C17, … |
| maximal normal subgroup of | C5×D103⋊C17, C7×D103⋊C17, C11×D103⋊C17 |
| maximal quotient of | C5×D103⋊C17, C5⋊(D103⋊C17), C7×D103⋊C17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3502, 1);