Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(C107⋊C8) |
| Sylow | C107 ⋊ C2×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D107 |
| commutator | C2×C107 | C22×C8 |
| Frattini | C2×C4 | C22×D107 |
| Fitting | C2×C42×C107 | C2 |
| socle | C23×C107 | C2×C4 |
| hypercenter | C2×C42 | D107 |
| hypocenter | C107 | C2×C4⋊C8 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
138 conjugacy classes of subgroups.
1736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28334295, #28334296, #28334301, … |
| maximal normal subgroup of | #28334295, #28334296, #28334301, … |
| maximal quotient of | C2×#20292378, C2×#20292380, #28335209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 570);