Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×#11724786 |
| Sylow | C109 ⋊ C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#89137 |
| commutator | C2×C109 | C22×C8 |
| Fitting | C2×Q8×C109 | C4 |
| socle | C22×C109 | C22×C4 |
| hypercenter | C2×Q8 | #89137 |
| hypocenter | C109 | C8×Q8 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
102 conjugacy classes of subgroups.
310 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#11724786, #28378616, Q16×#11724786, … |
| maximal normal subgroup of | SD16×#11724786, #28378616, Q16×#11724786, … |
| maximal quotient of | C4⋊C4×#11724786, #28379085, #28379129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1597);