Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#16863267 |
| Fitting | C22×C4⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#385 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C22×C67 | C23×C4 |
| Frattini | C23 | C23×D67 |
| Fitting | C22×C4⋊C4×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C22×C4⋊C4 | D67 |
| hypocenter | C67 | C2×#385 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
1232 conjugacy classes of subgroups.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30751209, #30751229, C4×#16863267, … |
| maximal normal subgroup of | #30751209, #30751229, C4×#16863267, … |
| maximal quotient of | C2×(C2×D67)⋊#95, C2×#22558440, C2×#22558441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6919);