Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×D127 |
| Fitting | C22×Q8×C127 ⋊ C2 |
| Sylow | C127 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D127 |
| commutator | C2×C127 | C25 |
| Frattini | C2 | C24×D127 |
| Fitting | C22×Q8×C127 | C2 |
| socle | C23×C127 | C23 |
| hypercenter | C22×Q8 | D127 |
| hypocenter | C127 | C23×Q8 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
850 conjugacy classes of subgroups.
1300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30638652, #30638663, #391×D127, … |
| maximal normal subgroup of | #30638652, #30638663, #391×D127, … |
| maximal quotient of | C22×C4⋊C4×D127, C2×C4×Q8×D127, C22×#16861174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1372);