Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D83 |
| commutator, socle | C2×C83 | C23×C4 |
| Fitting | C2×#41×C83 | C2 |
| hypercenter | C2×#41 | D83 |
| hypocenter | C83 | #568 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
258 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=e,e^2=f,d^a=df,g^a=g^82,c^b=cf854 conjugacy classes — view the full character table.
| maximal subgroup of | #24907682, #24907685, #24907701, … |
| maximal normal subgroup of | #24907682, #24907685, #24907701, … |
| maximal quotient of | #24915882, #24915891, #24915908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1316);