Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic548 |
| Sylow | C137 ⋊ C22×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D548 |
| commutator | C4×C137 | C24 |
| Frattini | C4 | C23×D137 |
| Fitting | C22×C8×C137 | C2 |
| socle | C23×C137 | D4 |
| hypercenter | C22×C8 | D137 |
| hypocenter | C137 | C22×Q16 |
| LCS | G ▷ C4×C137 ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
258 conjugacy classes of subgroups.
2204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31781129, #31781131, #31781648, … |
| maximal normal subgroup of | #31781129, #31781131, #31781648, … |
| maximal quotient of | C22×#17984013, C22×#17984022, C2×C4×Dic548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1326);