Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#14581800 |
| Fitting | C22×M16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#131 |
1504 conjugacy classes of subgroups; only the 821 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 821 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 | #35309817, #35309821, #35309835, … |
| maximal normal subgroup of | #35309817, #35309821, #35309835, … |
| maximal quotient of | C22×#19127658, C22×#19127659, C2×C4×#14581800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19216);