Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊(C107⋊C16) |
| Sylow | C107 ⋊ C22⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×D107 |
| commutator | C2×C107 | C2×C16 |
| Fitting | C22×C8×C107 | C2 |
| socle | C22×C107 | C2×C8 |
| hypercenter | C22×C8 | D107 |
| hypocenter | C107 | C22⋊C16 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,107|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^1061736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28334384, #28334385, #28334386, … |
| maximal normal subgroup of | #28334384, #28334385, #28334386, … |
| maximal quotient of | #28334385, #28334401, D4⋊(C107⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 329);