Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C137 ⋊ #384 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D137 |
| commutator | C22×C137 | C22×C4 |
| Fitting | C2×C42×C137 | C2 |
| socle | C23×C137 | C23 |
| hypercenter | C2×C42 | D137 |
| hypocenter | C137 | #384 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=d,c^2=e,b^a=bd,c^a=ce,g^a=g^1362204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778673, #31780789, #31780790, … |
| maximal normal subgroup of | #31778673, #31780789, #31780790, … |
| maximal quotient of | #31779019, #31779054, #31780941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 419);