Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×C107⋊C16 |
| derived, Sylow | C107 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D107 |
| commutator, hypocenter | C107 | C22×C16 |
| Frattini | C8 | C22×D107 |
| Fitting | C22×C8×C107 | C2 |
| socle | C23×C107 | C8 |
| LCS | G ▷ C107 | |
| UCS | C1 ◁ C22×C8 | |
98 conjugacy classes of subgroups.
1760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28334538, #28334539, #28334550, … |
| maximal normal subgroup of | #28334538, #28334539, #28334550, … |
| maximal quotient of | C2×C4×C107⋊C16, C2×C22⋊(C107⋊C16), C2×C4⋊(C107⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 961);