Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#19128011 |
| Sylow | C83 ⋊ C2×#479 |
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35412024, C4×#19128011, #35412098, … |
| maximal normal subgroup of | #35412024, C4×#19128011, #35412098, … |
| maximal quotient of | C2×#24907477, C2×#24907718, C2×#24907728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14290);