Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14524025 |
| Fitting | C22×C22⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×#123 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C22×C67 | C25 |
| Frattini | C22 | C24×D67 |
| Fitting | C22×C22⋊C4×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C22×C22⋊C4 | D67 |
| hypocenter | C67 | C22×#123 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
1968 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 605 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30747176, #30748440, #30748471, … |
| maximal normal subgroup of | #30747176, #30748440, #30748471, … |
| maximal quotient of | C22×#16863258, C22×#16863270, C22×#16863272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17742);