Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic109 |
| derived, Sylow | C109 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D109 |
| commutator, hypocenter | C109 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D109 |
| Fitting | C22×C8×C109 | C2 |
| socle | C23×C109 | C2×C4 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C22×C8 | |
162 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28361109, #28361113, C4×C8×Dic109, … |
| maximal normal subgroup of | #28361109, #28361113, C4×C8×Dic109, … |
| maximal quotient of | C2×C8×#11724784, C2×#20294748, C8×#13182013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 494);