Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16812696 |
| Fitting | C2×C42×C109 ⋊ C2 |
| Sylow | C109 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D109 |
| commutator | C22×C109 | C24 |
| Frattini | C22 | C23×D109 |
| Fitting | C2×C42×C109 | C2 |
| socle | C23×C109 | C23 |
| hypercenter | C2×C42 | D109 |
| hypocenter | C109 | C2×#127 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
1756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#20294769, #28361699, #28361701, … |
| maximal normal subgroup of | C2×#20294769, #28361699, #28361701, … |
| maximal quotient of | C2×#20294896, C2×#20294928, C4×#16812696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1089);