Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D83 |
| commutator | C2×C83 | C2×C42 |
| Fitting | #97×C83 | C2 |
| socle | C22×C83 | C22×C4 |
| hypercenter | #97 | D83 |
| hypocenter | C83 | C4×M16 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=d,b^2=e,d^2=f,c^a=cf,g^b=g^82,g^c=g^82860 conjugacy classes — view the full character table.
| maximal subgroup of | #24909273, C4×M16×D83, C2×#19127653, … |
| maximal normal subgroup of | #24909273, C4×M16×D83, C2×#19127653, … |
| maximal quotient of | #97×Dic83, #24907155, #24907210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 501);