Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #550 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D83 |
| commutator, socle | C22×C83 | C24 |
| Fitting | C4×Q8×C83 | C2 |
| hypercenter | C4×Q8 | D83 |
| hypocenter | C83 | #550 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
312 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|b^2=e,c^2=e,d^2=e,b^a=be,c^a=cf,g^a=g^82,d^b=de,g^c=g^82845 conjugacy classes — view the full character table.
| maximal subgroup of | #24906526, #24906530, #24906588, … |
| maximal normal subgroup of | #24906526, #24906530, #24906588, … |
| maximal quotient of | #24910301, Q8×C4⋊Dic83, #24910410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1221);