Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #100×C83 ⋊ C2 |
| Sylow | C83 ⋊ #413 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊C4×D83 |
| commutator | C22×C83 | C22×C4 |
| Frattini | C2×C4 | C22×D83 |
| Fitting | #100×C83 | C2 |
| socle | C2×C83 | C2×C22⋊C4 |
| hypercenter | #100 | D83 |
| hypocenter | C83 | #413 |
| LCS | G ▷ C22×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #100 | |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,e^b=ef,g^c=g^82473 conjugacy classes — view the full character table.
| maximal subgroup of | #24909101, #24909103, #24909111, … |
| maximal normal subgroup of | #24909101, #24909103, #24909111, … |
| maximal quotient of | #24907200, #100×Dic83, #24907258, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 530);