Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C137 ⋊ C2 |
| Sylow | C137 ⋊ #576 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D548 |
| commutator | C4×C137 | C24 |
| Frattini | C4 | C23×D137 |
| Fitting | #131×C137 | C2 |
| socle | C2×C137 | C22×D4 |
| hypercenter | #131 | D137 |
| hypocenter | C137 | #576 |
| LCS | G ▷ C4×C137 ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
268 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|e^2=f,b^a=be,e^a=ef,g^a=g^136,e^b=ef,g^b=g^136,d^c=df1382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31782744, #31782748, #31782758, … |
| maximal normal subgroup of | #31782744, #31782748, #31782758, … |
| maximal quotient of | #31789316, #31789389, #31789623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1354);