Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C107 ⋊ #444 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×D107 |
| commutator | C4×C107 | C22×C4 |
| Frattini | C2×C4 | C22×D107 |
| Fitting | #135×C107 | C2 |
| socle | C2×C107 | C4×D4 |
| hypercenter | #135 | D107 |
| hypocenter | C107 | #444 |
| LCS | G ▷ C4×C107 ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #135 | |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^106,d^b=df,g^c=g^106764 conjugacy classes — view the full character table.
| maximal subgroup of | #28338349, #28338353, #28338356, … |
| maximal normal subgroup of | #28338349, #28338353, #28338356, … |
| maximal quotient of | SD16⋊(C107⋊C8), #28335280, #28335285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 671);