Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×Dic274 |
| Sylow | C137 ⋊ C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D137 |
| commutator | C2×C137 | C22×C8 |
| Frattini | C2×C4 | C22×D137 |
| Fitting | C4×C8×C137 | C2 |
| socle | C22×C137 | C22×C4 |
| hypercenter | C4×C8 | D137 |
| hypocenter | C137 | C8×Q8 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 | |
102 conjugacy classes of subgroups.
2216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778767, #31778769, C8×#14555498, … |
| maximal normal subgroup of | #31778767, #31778769, C8×#14555498, … |
| maximal quotient of | C8×C4⋊Dic137, C8×#14555489, #31781345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 674);