Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C2×C22⋊C8×D67 |
| Fitting | C2×C22⋊C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×C22⋊C8 |
1072 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1280×D67, #30745423, #30745441, … |
| maximal normal subgroup of | #1280×D67, #30745423, #30745441, … |
| maximal quotient of | C2×#323×D67, C2×#324×D67, #1458×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12940);