Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C83 ⋊ #330 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | (C2×D83)⋊C4 |
| commutator | C2×C4×C83 | C2×C4 |
| Frattini | C42 | C2×D83 |
| Fitting | #97×C83 | C2 |
| socle | C22×C83 | C22⋊C4 |
| hypercenter | #97 | D83 |
| hypocenter | C83 | #330 |
| LCS | G ▷ C2×C4×C83 ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=d,b^2=e,c^2=f,d^2=e,b^a=bc,c^a=ce,c^b=cf,d^b=def,g^b=g^82839 conjugacy classes — view the full character table.
| maximal subgroup of | #24906754, #24906757, #24906759, … |
| maximal normal subgroup of | #24906754, #24906757, #24906759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 290);