Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #335 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22⋊D83 |
| commutator | C4×C83 | C2×C8 |
| Frattini | C42 | C2×D83 |
| Fitting | C4⋊C8×C83 | C2 |
| socle | C22×C83 | C4⋊C4 |
| hypercenter | C4⋊C8 | D83 |
| hypocenter | C83 | #335 |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=d,b^2=ce,c^2=e,d^2=f,b^a=bc,c^a=ce,g^b=g^82848 conjugacy classes — view the full character table.
| maximal subgroup of | #24906339, #24906341, #24906344, … |
| maximal normal subgroup of | #24906339, #24906341, #24906344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 301);