Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C107 ⋊ #350 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22⋊D107 |
| commutator | C4×C107 | C2×C8 |
| Frattini | C2×C8 | C2×D107 |
| Fitting | #131×C107 | C2 |
| socle | C2×C107 | C22⋊C8 |
| hypercenter | #131 | D107 |
| hypocenter | C107 | #350 |
| LCS | G ▷ C4×C107 ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #131 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^106,c^b=cf,d^b=df1088 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D107, C2×#20292411, #28338087, … |
| maximal normal subgroup of | #350×D107, C2×#20292411, #28338087, … |
| maximal quotient of | #28334387, #28334403, D4⋊(C107⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 333);