Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #131×D83 |
| Fitting | #131×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22×D83 |
| commutator, socle | C2×C83 | C23×C4 |
| Frattini | C4 | C23×D83 |
| Fitting | #131×C83 | C2 |
| hypercenter | #131 | D83 |
| hypocenter | C83 | C2×#131 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C8 ◁ #131 | |
266 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
860 conjugacy classes — view the full character table.
| maximal subgroup of | #350×D83, #24909089, #443×D83, … |
| maximal normal subgroup of | #350×D83, #24909089, #443×D83, … |
| maximal quotient of | #405×D83, #131×Dic83, #24915885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1310);