Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#11724784 |
| derived, Sylow | C109 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D109 |
| commutator, hypocenter | C109 | C82 |
| Frattini | C42 | C2×D109 |
| Fitting | C4×C8×C109 | C2 |
| socle | C22×C109 | C42 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C4×C8 | |
74 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#11724784, #28360948, #28360951, … |
| maximal normal subgroup of | C16×#11724784, #28360948, #28360951, … |
| maximal quotient of | #28360859, C16×#11724784, C8×#13182004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 269);