Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#16812605 |
| derived, Sylow | C109 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D109 |
| commutator, hypocenter | C109 | C2×C32 |
| Frattini | C16 | C2×D109 |
| Fitting | C2×C16×C109 | C2 |
| socle | C22×C109 | C16 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C16 | |
34 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic109, C4×#16812605, #28361165, … |
| maximal normal subgroup of | C32×Dic109, C4×#16812605, #28361165, … |
| maximal quotient of | C4×#16812605, C22⋊#16812605, C4⋊#16812605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 381);