Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19127446 |
| Sylow | C83 ⋊ C2×#332 |
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 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.
1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295351, C4×#19127446, #35295364, … |
| maximal normal subgroup of | #35295351, C4×#19127446, #35295364, … |
| maximal quotient of | C2×#24905285, #35292381, #35292683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3153);