Finite Group DatabasebetaFinite Group Databasebeta| order | 6848 |
| isoclinism | isoclinic class of D107 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×D107 |
| Fitting | C32×C107 ⋊ C2 |
| derived, Sylow | C107 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D107 |
| commutator, hypocenter | C107 | C2×C32 |
| Frattini | C16 | C2×D107 |
| Fitting | C32×C107 | C2 |
| socle | C2×C107 | C2×C16 |
| LCS | G ▷ C107 | |
| UCS | C1 ◁ C32 | |
34 conjugacy classes of subgroups.
1760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D107, #28334671, C2×C32×D107, … |
| maximal normal subgroup of | C64×D107, #28334671, C2×C32×D107, … |
| maximal quotient of | C32×Dic107, (C2×D107)⋊C32, Dic107⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6848, 380);