Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C137 ⋊ #431 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#10587739 |
| commutator | C2×C137 | C22×C8 |
| Frattini | C22 | C22×#10587739 |
| Fitting | C42×C137 | C4 |
| socle | C22×C137 | C22×C4 |
| hypercenter | C42 | #10587739 |
| hypocenter | C137 | #431 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^100,g^b=g^136,g^c=g^136,g^e=g^136584 conjugacy classes — view the full character table.
| maximal subgroup of | #31795616, #31795621, #31795644, … |
| maximal normal subgroup of | #31795616, #31795621, #31795644, … |
| maximal quotient of | #31796504, C4×#17984145, C4×C4⋊#11764047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1568);