Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #41×#89137 |
| Fitting | #41×C109 ⋊ C4 |
| Sylow | C109 ⋊ C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#89137 |
| commutator, socle | C2×C109 | C23×C4 |
| Frattini | C2 | C23×#89137 |
| Fitting | #41×C109 | C4 |
| hypercenter | #41 | #89137 |
| hypocenter | C109 | C4×#41 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C4 ◁ #41 | |
310 conjugacy classes of subgroups.
310 conjugacy classes — view the full character table.
| maximal subgroup of | #104×#89137, #28378797, #28379069, … |
| maximal normal subgroup of | #104×#89137, #28378797, #28379069, … |
| maximal quotient of | #117×#89137, C4×D4×#89137, C4×Q8×#89137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1615);