Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4⋊C4×#10587739 |
| Fitting | C4⋊C4×C137 ⋊ C4 |
| Sylow | C137 ⋊ C4×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#10587739 |
| commutator | C2×C137 | C2×C42 |
| Fitting | C4⋊C4×C137 | C4 |
| socle | C22×C137 | C22×C4 |
| hypercenter | C4⋊C4 | #10587739 |
| hypocenter | C137 | C4×C4⋊C4 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
194 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
380 conjugacy classes — view the full character table.
| maximal subgroup of | #102×#10587739, #103×#10587739, #31796560, … |
| maximal normal subgroup of | #102×#10587739, #103×#10587739, #31796560, … |
| maximal quotient of | #95×#10587739, #31795964, #31795966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1489);