Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16812745 |
| Fitting | C2×#41×C109 ⋊ C2 |
| Sylow | C109 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D109 |
| commutator | C2×C109 | C25 |
| Frattini | C2 | C24×D109 |
| Fitting | C2×#41×C109 | C2 |
| socle | C22×C109 | C24 |
| hypercenter | C2×#41 | D109 |
| hypocenter | C109 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1114 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28362984, #28362987, #28363000, … |
| maximal normal subgroup of | #28362984, #28362987, #28363000, … |
| maximal quotient of | C2×#20295498, C2×#20295500, C2×#20295506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1380);