Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#100×D83 |
| Fitting | C2×#100×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#100 |
992 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #1390×D83, #35319349, #35321880, … |
| maximal normal subgroup of | #1390×D83, #35319349, #35321880, … |
| maximal quotient of | C2×#323×D83, #1460×D83, C2×#24905782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12975);