Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #97×C137 ⋊ C2 |
| Sylow | C137 ⋊ #490 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D548 |
| commutator | C2×C4×C137 | C23 |
| Frattini | C2×C4 | C22×D137 |
| Fitting | #97×C137 | C2 |
| socle | C22×C137 | C2×D4 |
| hypercenter | #97 | D137 |
| hypocenter | C137 | #490 |
| LCS | G ▷ C2×C4×C137 ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^136,c^b=cf1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778821, #31780083, #31780088, … |
| maximal normal subgroup of | #31778821, #31780083, #31780088, … |
| maximal quotient of | #31780923, #31781486, #31781613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 914);