Finite Group DatabasebetaFinite Group Databasebeta| order | 8752 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic547 |
| unambiguous semidirect product | C547⋊C42 |
| derived, Sylow | C547 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D547 |
| commutator, hypocenter | C547 | C42 |
| Frattini | C22 | C2×D547 |
| Fitting | C2×C4×C547 | C2 |
| socle | C22×C547 | C22 |
| LCS | G ▷ C547 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
2200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic547, #31775912, #31775928, … |
| maximal normal subgroup of | C8×Dic547, #31775912, #31775928, … |
| maximal quotient of | C547⋊#95, C8×Dic547, C4×C547⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8752, 16);