Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | 2−1+4×C107 ⋊ C2 |
| Sylow | C107 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D107 |
| commutator, socle | C2×C107 | C25 |
| Fitting | 2−1+4×C107 | C2 |
| hypercenter | 2−1+4 | D107 |
| hypocenter | C107 | #585 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
810 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|e^2=f,b^a=bf,d^a=df,c^b=cf,g^c=g^106,g^d=g^106,g^e=g^106935 conjugacy classes — view the full character table.
| maximal subgroup of | #28345808, #28345813, #28345831, … |
| maximal normal subgroup of | #28345808, #28345813, #28345831, … |
| maximal quotient of | #28349661, #28349663, #28349667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 1386);