Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#13182032 |
| derived, Sylow | C109 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #89137 |
| commutator, hypocenter | C109 | C22×C16 |
| Frattini | C4 | C22×#89137 |
| Fitting | C22×C4×C109 | C4 |
| socle | C23×C109 | C8 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C22×C4 | |
98 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | #28378070, #28378071, #28378086, … |
| maximal normal subgroup of | #28378070, #28378071, #28378086, … |
| maximal quotient of | C2×C4×#13182032, C2×C22⋊#13182032, C2×C4⋊#13182032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1602);