Finite Group DatabasebetaFinite Group Databasebeta| order | 8752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D547 |
| Fitting | C2×C4×C547 ⋊ C2 |
| derived, Sylow | C547 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D547 |
| commutator, hypocenter | C547 | C22×C4 |
| Frattini | C2 | C22×D547 |
| Fitting | C2×C4×C547 | C2 |
| socle | C22×C547 | C22 |
| LCS | G ▷ C547 | |
| UCS | C1 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
2200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D547)⋊C8, C42×D547, C22⋊C4×D547, … |
| maximal normal subgroup of | (C2×D547)⋊C8, C42×D547, C22⋊C4×D547, … |
| maximal quotient of | C42×D547, C2×C4×Dic547, C22⋊C4×D547, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8752, 32);