Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | Aut(G) order 3683232 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3654 |
| direct product | C2×D1827 |
| unambiguous semidirect product | (C2×C7)⋊D261 |
| unambiguous semidirect product | (C2×C9)⋊D203 |
| unambiguous semidirect product | (C2×C29)⋊D63 |
| Fitting | C2×C7×C9×C29 ⋊ C2 |
| derived, Hall | C7×C9×C29 ⋊ C22 |
| Hall | C9×C29 ⋊ C2×D7 |
| Hall | C7×C29 ⋊ C2×D9 |
| Hall | C7×C9 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×D63 |
| Sylow | C9 ⋊ C2×D203 |
| Sylow | C7 ⋊ C2×D261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1827 |
| commutator, hypocenter | C7×C9×C29 | C22 |
| Frattini | C3 | C2×D609 |
| Fitting | C2×C7×C9×C29 | C2 |
| socle | C2×C3×C7×C29 | D3 |
| LCS | G ▷ C7×C9×C29 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
1830 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1827, C2×D9135, C2×C5×D1827, … |
| maximal normal subgroup of | C2×C5×D1827, D7308 |
| maximal quotient of | D5×D1827, C2×D9135, C2×C5×D1827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 52);