Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#19127564 |
| Sylow | C83 ⋊ C2×#381 |
1144 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 389 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 | #35294015, #35294017, C2×#24905316, … |
| maximal normal subgroup of | #35294015, #35294017, C2×#24905316, … |
| maximal quotient of | C2×#24905686, C2×#24905690, C4×#19127564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6887);