Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#13182028 |
| Fitting | C22×D4×C109 ⋊ C2 |
| Sylow | C109 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D109 |
| commutator | C2×C109 | C25 |
| Frattini | C2 | C24×D109 |
| Fitting | C22×D4×C109 | C2 |
| socle | C23×C109 | C23 |
| hypercenter | C22×D4 | D109 |
| hypocenter | C109 | C22×#41 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
890 conjugacy classes of subgroups.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28362948, #28362957, #28362969, … |
| maximal normal subgroup of | #28362948, #28362957, #28362969, … |
| maximal quotient of | C22×#16812655, C22×#16812657, C22×#16812659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1375);