Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×C4×(C2×D67)⋊C4 |
| Fitting | C22×C42×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×C4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D67 |
| commutator | C2×C67 | C22×C42 |
| Frattini | C23 | C23×D67 |
| Fitting | C22×C42×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C22×C42 | D67 |
| hypocenter | C67 | C2×C4×C22⋊C4 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C42 | |
1360 conjugacy classes of subgroups.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#16863119, #30746342, #30748485, … |
| maximal normal subgroup of | C4×#16863119, #30746342, #30748485, … |
| maximal quotient of | C2×C4×C67⋊#95, C42×(C2×D67)⋊C4, C2×(C2×D67)⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6841);