Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16812678 |
| Sylow | C109 ⋊ C2×C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D109 |
| commutator | C22×C109 | C24 |
| Frattini | C22 | C23×D109 |
| Fitting | C23×C4×C109 | C2 |
| socle | C23×C109 | C23 |
| hypercenter | C23×C4 | D109 |
| hypocenter | C109 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
322 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28361395, #28361397, C2×#20294762, … |
| maximal normal subgroup of | #28361395, #28361397, C2×#20294762, … |
| maximal quotient of | C2×#20294886, C2×#20294899, C2×#20294910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1047);