Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#41×D127 |
| Fitting | C2×#41×C127 ⋊ C2 |
| Sylow | C127 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D127 |
| commutator | C2×C127 | C25 |
| Frattini | C2 | C24×D127 |
| Fitting | C2×#41×C127 | C2 |
| socle | C22×C127 | C24 |
| hypercenter | C2×#41 | D127 |
| hypocenter | C127 | C22×#41 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30638672, #408×D127, #30647172, … |
| maximal normal subgroup of | #30638672, #408×D127, #30647172, … |
| maximal quotient of | C2×#117×D127, C2×C4×D4×D127, C2×C4×Q8×D127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1374);