Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | #346×D83 |
| Fitting | #346×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#346 |
200 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1313×D83, #35313407, #35313411, … |
| maximal normal subgroup of | #1313×D83, #35313407, #35313411, … |
| maximal quotient of | #1311×D83, #1312×D83, #35313420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6098);