Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊D203 |
| Fitting, socle, derived, Hall | C32×C7×C29 ⋊ C22 |
| Hall | C32×C29 ⋊ C2×D7 |
| Hall | C7×C29 ⋊ D32 |
| Hall | C32×C7 ⋊ C2×D29 |
| Sylow | C29 ⋊ (C3⋊D3)⋊D7 |
| Sylow | C32 ⋊ C2×D203 |
| Sylow | C7 ⋊ (C3⋊D3)⋊D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C29 | C22 |
| LCS | G ▷ C32×C7×C29 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,7,29|d^a=d^2,e^a=e^6,f^a=f^28,c^b=c^2,d^b=d^2615 conjugacy classes — view the full character table.
| maximal subgroup of | C5×(C3⋊D3)⋊D203, #49141614, (C3⋊D3)⋊D1015 |
| maximal normal subgroup of | C5×(C3⋊D3)⋊D203 |
| maximal quotient of | C5×(C3⋊D3)⋊D203, #49141614, (C3⋊D3)⋊D1015 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 145);