Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#14581814 |
| Fitting | C2×C4×C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×#135 |
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35314142, #35314145, #35314147, … |
| maximal normal subgroup of | #35314142, #35314145, #35314147, … |
| maximal quotient of | C8×#14581814, #35373937, #35374155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13284);