Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D428 |
| Fitting | C23×C4×C107 ⋊ C2 |
| Sylow | C107 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D107 |
| commutator | C2×C107 | C25 |
| Frattini | C2 | C24×D107 |
| Fitting | C23×C4×C107 | C2 |
| socle | C24×C107 | C22 |
| hypercenter | C23×C4 | D107 |
| hypocenter | C107 | C23×D4 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
1736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28334701, #28336381, #28336391, … |
| maximal normal subgroup of | #28334701, #28336381, #28336391, … |
| maximal quotient of | C23×(C2×D107)⋊C4, C23×C4⋊Dic107, C22×C4×D428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 1371);