Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16812628 |
| Sylow | C109 ⋊ C2×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D109 |
| commutator | C2×C109 | C22×C8 |
| Frattini | C2×C4 | C22×D109 |
| Fitting | C22×C8×C109 | C2 |
| socle | C23×C109 | C2×C4 |
| hypercenter | C22×C8 | D109 |
| hypocenter | C109 | C2×C4⋊C8 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
138 conjugacy classes of subgroups.
1768 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28360971, #28362880, C4×#16812628, … |
| maximal normal subgroup of | #28360971, #28362880, C4×#16812628, … |
| maximal quotient of | C2×#20294776, C2×#20294778, #28361778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 569);