Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#19127560 |
| Fitting | C2×#95×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#380 |
1232 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35294022, #35294406, #35294434, … |
| maximal normal subgroup of | #35294022, #35294406, #35294434, … |
| maximal quotient of | C2×(C2×D83)⋊#95, C2×#24905688, C2×Dic83⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6882);