Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | C139⋊#564 |
| Sylow | C139 ⋊ #564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D139 |
| commutator, socle | C22×C139 | C24 |
| Fitting | #125×C139 | C2 |
| hypercenter | #125 | D139 |
| hypocenter | C139 | #564 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ #125 | |
172 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,139|a^2=e,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,g^d=g^138985 conjugacy classes — view the full character table.
| maximal subgroup of | #31805705, #31805707, #31805730, … |
| maximal normal subgroup of | #31805705, #31805707, #31805730, … |
| maximal quotient of | #31809586, #31809587, #31809588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 1304);