Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16861198 |
| Fitting | C22×Q8×C127 ⋊ C2 |
| Sylow | C127 ⋊ C2×#124 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D127 |
| commutator | C22×C127 | C24 |
| Frattini | C22 | C23×D127 |
| Fitting | C22×Q8×C127 | C2 |
| socle | C23×C127 | C23 |
| hypercenter | C22×Q8 | D127 |
| hypocenter | C127 | C2×#124 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
330 conjugacy classes of subgroups.
1288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30639115, #30639131, #30639133, … |
| maximal normal subgroup of | #30639115, #30639131, #30639133, … |
| maximal quotient of | C2×#22549741, C2×#22549766, C2×#22549777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1067);