Finite Group DatabasebetaFinite Group Databasebeta| order | 9028 |
| automorphism | Aut(G) order 9750240 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4514 |
| direct product | C2×D2257 |
| unambiguous semidirect product | (C2×C37)⋊D61 |
| unambiguous semidirect product | (C2×C61)⋊D37 |
| Fitting, socle | C2×C37×C61 ⋊ C2 |
| derived, Hall | C37×C61 ⋊ C22 |
| Sylow | C61 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2257 |
| commutator, hypocenter | C37×C61 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C61 | C2 |
| LCS | G ▷ C37×C61 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#27214379, C2×#27214378, C2×(C37⋊C3)⋊D61, … |
| maximal normal subgroup of | C2×#27214379, C2×#27214378, C2×(C37⋊C3)⋊D61, … |
| maximal quotient of | D3×D2257, C2×C3×D2257, C2×D6771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9028, 13);