Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C139 ⋊ C2 |
| Sylow | C139 ⋊ #444 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×D139 |
| commutator | C4×C139 | C22×C4 |
| Frattini | C2×C4 | C22×D139 |
| Fitting | #108×C139 | C2 |
| socle | C2×C139 | C4×D4 |
| hypercenter | #108 | D139 |
| hypocenter | C139 | #444 |
| LCS | G ▷ C4×C139 ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #108 | |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,139|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^138,g^c=g^138988 conjugacy classes — view the full character table.
| maximal subgroup of | #31808294, #31808298, #31808301, … |
| maximal normal subgroup of | #31808294, #31808298, #31808301, … |
| maximal quotient of | #31805215, #31805222, #31805227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 670);