Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| isoclinism | isoclinic class of D107 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic107 |
| derived, Sylow | C107 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D107 |
| commutator, hypocenter | C107 | C24×C4 |
| Frattini | C2 | C24×D107 |
| Fitting, socle | C25×C107 | C2 |
| LCS | G ▷ C107 | |
| UCS | C1 ◁ C25 | |
1362 conjugacy classes of subgroups.
1760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28334683, C22×C107⋊#95, C2×C22⋊C4×Dic107, … |
| maximal normal subgroup of | #28334683, C22×C107⋊#95, C2×C22⋊C4×Dic107, … |
| maximal quotient of | C23×C4×Dic107, C23×C22⋊Dic107, C23×C4⋊Dic107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 1368);