Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14581771 |
| Sylow | C83 ⋊ C22×C22⋊Q8 |
1840 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 725 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 | #35295763, #35295848, #35295850, … |
| maximal normal subgroup of | #35295763, #35295848, #35295850, … |
| maximal quotient of | C22×#19127561, C22×#19127574, C22×#19127585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17738);