Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#13133801 |
| Fitting | C4×C8×C107 ⋊ C2 |
| Sylow | C107 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D107 |
| commutator | C2×C107 | C2×C42 |
| Frattini | C2×C4 | C22×D107 |
| Fitting | C4×C8×C107 | C2 |
| socle | C22×C107 | C22×C4 |
| hypercenter | C4×C8 | D107 |
| hypocenter | C107 | C4×M16 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
142 conjugacy classes of subgroups.
1736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13133801, #28334740, #28334747, … |
| maximal normal subgroup of | C8×#13133801, #28334740, #28334747, … |
| maximal quotient of | C8×#13133801, #28334747, #28334755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 499);