Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D107 |
| Fitting | M32×C107 ⋊ C2 |
| Sylow | C107 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D107 |
| commutator, socle | C2×C107 | C22×C8 |
| Fitting | M32×C107 | C2 |
| hypercenter | M32 | D107 |
| hypocenter | C107 | C2×M32 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
1100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×D107, #28338064, #349×D107, … |
| maximal normal subgroup of | #347×D107, #28338064, #349×D107, … |
| maximal quotient of | #346×D107, M32×Dic107, #28338054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 962);