Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | #338×D67 |
| Fitting | #338×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#338 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C42×D67 |
| commutator | C4×C67 | C2×C42 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #338×C67 | C2 |
| socle | C2×C67 | C2×#95 |
| hypercenter | #338 | D67 |
| hypocenter | C67 | C2×#338 |
| LCS | G ▷ C4×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ #338 | |
372 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #1341×D67, #1342×D67, #30765991, … |
| maximal normal subgroup of | #1341×D67, #1342×D67, #30765991, … |
| maximal quotient of | #1275×D67, #30745248, #30745251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4212);