Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×H(5,𝔽2)×D83 |
| Fitting | C2×H(5,𝔽2)×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×H(5,𝔽2) |
6560 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1790×D83, #35403669, #1792×D83, … |
| maximal normal subgroup of | #1790×D83, #35403669, #1792×D83, … |
| maximal quotient of | C2×#518×D83, C2×#520×D83, C4×H(5,𝔽2)×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19310);