Finite Group DatabasebetaFinite Group Databasebeta| order | 7203 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #3861⋊C49 |
| Fitting, Sylow | C72⋊C49 ⋊ C3 |
| derived | C72 ⋊ C3×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #3861⋊C7 |
| commutator, hypocenter | C72 | C3×C49 |
| Frattini, socle | C72 | C7×ΓL(1,𝔽8) |
| Fitting | C72⋊C49 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C7 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
3,7^4|b^7=e,c^a=c^4,d^a=d^4,c^b=cd259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7203, 20);