Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C83 ⋊ #347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×Dic83 |
| commutator | C4×C83 | C42 |
| Frattini | C2×C8 | C2×D83 |
| Fitting | M32×C83 | C2 |
| socle | C2×C83 | #97 |
| hypercenter | M32 | D83 |
| hypocenter | C83 | #347 |
| LCS | G ▷ C4×C83 ▷ C83 | |
| UCS | C1 ◁ C4 ◁ M32 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,c^b=cf,g^b=g^82842 conjugacy classes — view the full character table.
| maximal subgroup of | #347×D83, C2×#19127478, #24909066, … |
| maximal normal subgroup of | #347×D83, C2×#19127478, #24909066, … |
| maximal quotient of | C2×#19127478 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 326);