Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D83 |
| commutator | C2×C83 | C23×C4 |
| Fitting | C4×Q8×C83 | C2 |
| socle | C22×C83 | C24 |
| hypercenter | C4×Q8 | D83 |
| hypocenter | C83 | #520 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
294 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=f,d^2=e,b^a=be,d^a=de,c^b=ce,g^b=g^82,g^c=g^82,g^d=g^82854 conjugacy classes — view the full character table.
| maximal subgroup of | #24916290, #24916294, #24916301, … |
| maximal normal subgroup of | #24916290, #24916294, #24916301, … |
| maximal quotient of | #24909817, #24909823, #24909828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1031);