Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| isoclinism | isoclinic class of #89137 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×#89137 |
| Fitting | C2×C8×C109 ⋊ C4 |
| derived, Sylow | C109 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #89137 |
| commutator, hypocenter | C109 | C2×C4×C8 |
| Frattini | C4 | C22×#89137 |
| Fitting | C2×C8×C109 | C4 |
| socle | C22×C109 | C42 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C8 | |
162 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#89137)⋊C16, #28378075, C4×C8×#89137, … |
| maximal normal subgroup of | (C2×#89137)⋊C16, #28378075, C4×C8×#89137, … |
| maximal quotient of | C2×C8×#11724786, C8×D109⋊C8, C2×#11724786⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1503);