Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | C2×#19127547 |
| Sylow | C83 ⋊ C2×#376 |
840 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#24905291, #35293805, #35293994, … |
| maximal normal subgroup of | C2×#24905291, #35293805, #35293994, … |
| maximal quotient of | C2×C4×C83⋊#95, C4×#19127547, C2×#24905688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6837);