Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic508 |
| Sylow | C127 ⋊ C22×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D508 |
| commutator | C4×C127 | C24 |
| Frattini | C4 | C23×D127 |
| Fitting | C22×C8×C127 | C2 |
| socle | C23×C127 | D4 |
| hypercenter | C22×C8 | D127 |
| hypocenter | C127 | C22×Q16 |
| LCS | G ▷ C4×C127 ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
258 conjugacy classes of subgroups.
2044 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30639070, #30639072, #30639589, … |
| maximal normal subgroup of | #30639070, #30639072, #30639589, … |
| maximal quotient of | C22×#16861134, C22×#16861143, C2×C4×Dic508, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1326);