Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×#11764049 |
| commutator, socle | C2×C137 | C22×C8 |
| Frattini | C2 | C22×#11764049 |
| Fitting | C2×C4×C137 | C8 |
| hypercenter | C2×C4 | #11764049 |
| hypocenter | C137 | C2×M32 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^127,g^c=g^136,g^d=g^100,g^e=g^136176 conjugacy classes — view the full character table.
| maximal subgroup of | #31797861, #31797862, #31797863, … |
| maximal normal subgroup of | #31797861, #31797862, #31797863, … |
| maximal quotient of | #31797945, C4×#17984184, C4×#17984185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1668);