Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D137⋊#131 |
| Sylow | C137 ⋊ C2×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#10587739 |
| commutator, socle | C2×C137 | C23×C4 |
| Frattini | C2 | C23×#10587739 |
| Fitting | #41×C137 | C4 |
| hypercenter | #41 | #10587739 |
| hypocenter | C137 | C2×#131 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C4 ◁ #41 | |
266 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,e^2=f,g^a=g^100,c^b=cf,g^d=g^136,g^e=g^136380 conjugacy classes — view the full character table.
| maximal subgroup of | #31796565, #31796569, #31796828, … |
| maximal normal subgroup of | #31796565, #31796569, #31796828, … |
| maximal quotient of | #31797349, C4×#17984175, C4×#17984176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1625);