Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#14523965 |
| Fitting | C2×C4×C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C4×#102 |
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30746592, C8×#14523965, #30746606, … |
| maximal normal subgroup of | #30746592, C8×#14523965, #30746606, … |
| maximal quotient of | C4×#16863125, #30746454, #30746469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4326);