Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C137 ⋊ C2 |
| Sylow | C137 ⋊ #431 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D137 |
| commutator | C2×C137 | C22×C8 |
| Frattini | C2×C4 | C22×D137 |
| Fitting | C4×C8×C137 | C2 |
| socle | C22×C137 | C22×C4 |
| hypercenter | C4×C8 | D137 |
| hypocenter | C137 | #431 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^1362216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14555493, #31779068, #31779071, … |
| maximal normal subgroup of | C8×#14555493, #31779068, #31779071, … |
| maximal quotient of | #31780534, C4×#17984000, C4×#17984017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 600);