Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C137 ⋊ #347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×#10587739 |
| commutator | C4×C137 | C42 |
| Frattini | C2×C4 | C2×#10587739 |
| Fitting | C2×C8×C137 | C4 |
| socle | C2×C137 | #97 |
| hypercenter | C2×C8 | #10587739 |
| hypocenter | C137 | #347 |
| LCS | G ▷ C4×C137 ▷ C137 | |
| UCS | C1 ◁ C4 ◁ C2×C8 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,g^a=g^100,c^b=cf,g^b=g^136,g^c=g^136566 conjugacy classes — view the full character table.
| maximal subgroup of | #31797006, C2×#22578296, #31797011, … |
| maximal normal subgroup of | #31797006, C2×#22578296, #31797011, … |
| maximal quotient of | #31795707, #31795831, C2×#22578296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1442);