Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#14581817 |
| Fitting | C2×#41×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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 | #24907837, #24907839, #24907941, … |
| maximal normal subgroup of | #24907837, #24907839, #24907941, … |
| maximal quotient of | C2×#19127705, C2×#19127702, C2×#19127744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1335);