Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C24 |
| direct product | C2×#126×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C83 |
| prime radical | C24×C83 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ G | |
246 conjugacy classes of subgroups.
2324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#1473, C4×#126×C83, C83×#2334, … |
| maximal normal subgroup of | C83×#1473, C4×#126×C83, C83×#2334, … |
| maximal quotient of | C2×#383×C83, C2×#387×C83, C2×#388×C83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 209);