Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19127512 |
| Fitting | C2×M32×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#360 |
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319651, C4×#19127512, #35319696, … |
| maximal normal subgroup of | #35319651, C4×#19127512, #35319696, … |
| maximal quotient of | C2×#24905431, C2×#24905434, #35314176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6243);