Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #500×D67 |
| Fitting | #500×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#500 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #500×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #500 | D67 |
| hypocenter | C67 | C2×#500 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 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 | #1364×D67, #1365×D67, #30767120, … |
| maximal normal subgroup of | #1364×D67, #1365×D67, #30767120, … |
| maximal quotient of | #1845×D67, #1942×D67, #1990×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15015);