Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×C107⋊C8 |
| unambiguous semidirect product | C107⋊C82 |
| derived, Sylow | C107 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D107 |
| commutator, hypocenter | C107 | C82 |
| Frattini | C42 | C2×D107 |
| Fitting | C4×C8×C107 | C2 |
| socle | C22×C107 | C42 |
| LCS | G ▷ C107 | |
| UCS | C1 ◁ C4×C8 | |
74 conjugacy classes of subgroups.
1760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C107⋊C8, #28334377, #28334380, … |
| maximal normal subgroup of | C16×C107⋊C8, #28334377, #28334380, … |
| maximal quotient of | C107⋊#1273, C16×C107⋊C8, C8×C107⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 269);