Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #334 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D548 |
| commutator | C4×C137 | C2×C8 |
| Frattini | C42 | C2×D137 |
| Fitting | C4×C8×C137 | C2 |
| socle | C22×C137 | C4⋊C4 |
| hypercenter | C4×C8 | D137 |
| hypocenter | C137 | #334 |
| LCS | G ▷ C4×C137 ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ C4×C8 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=c,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^1362204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778756, #31778757, #31778759, … |
| maximal normal subgroup of | #31778756, #31778757, #31778759, … |
| maximal quotient of | #31778624, #31778853, #31778855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 300);