Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#14581706 |
| Fitting | C2×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
842 conjugacy classes — view the full character table.
| maximal subgroup of | #24907250, C4×#14581706, #24907376, … |
| maximal normal subgroup of | #24907250, C4×#14581706, #24907376, … |
| maximal quotient of | C2×#19127467, C4×#14581706, #24907377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 519);