Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×D127 |
| Fitting | C4⋊Q8×C127 ⋊ C2 |
| Sylow | C127 ⋊ C2×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D127 |
| commutator, socle | C22×C127 | C24 |
| Fitting | C4⋊Q8×C127 | C2 |
| hypercenter | C4⋊Q8 | D127 |
| hypocenter | C127 | C2×C4⋊Q8 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
290 conjugacy classes of subgroups.
910 conjugacy classes — view the full character table.
| maximal subgroup of | #332×D127, #333×D127, #30637400, … |
| maximal normal subgroup of | #332×D127, #333×D127, #30637400, … |
| maximal quotient of | #384×D127, #389×D127, #391×D127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1090);