Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×D4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D83 |
| commutator, socle | C23×C83 | C23 |
| Fitting | C22×D4×C83 | C2 |
| hypercenter | C22×D4 | D83 |
| hypocenter | C83 | #392 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
322 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,83|b^a=bd,c^a=ce,c^b=cf,g^c=g^82842 conjugacy classes — view the full character table.
| maximal subgroup of | #24906379, #24906384, #24906406, … |
| maximal normal subgroup of | #24906379, #24906384, #24906406, … |
| maximal quotient of | #24908458, #24908459, #24908463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 457);