Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#19127709 |
| Sylow | C83 ⋊ C2×#419 |
752 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309894, #35309896, #35309955, … |
| maximal normal subgroup of | #35309894, #35309896, #35309955, … |
| maximal quotient of | C2×#24905857, C2×#24905909, #35370850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13015);