Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#17984133 |
| Fitting | C22×D4×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D137 |
| commutator | C2×C137 | C25 |
| Frattini | C2 | C24×D137 |
| Fitting | C22×D4×C137 | C2 |
| socle | C22×C137 | C24 |
| hypercenter | C22×D4 | D137 |
| hypocenter | C137 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1394 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31780735, #31780736, #31780742, … |
| maximal normal subgroup of | #31780735, #31780736, #31780742, … |
| maximal quotient of | C2×#22577875, C2×#22577876, C2×#22577878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1379);