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×C4 |
| direct product | C2×#124×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C83 |
| prime radical | C22×D4×C83 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ G | |
330 conjugacy classes of subgroups.
2324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#1469, C2×#329×C83, C83×#1527, … |
| maximal normal subgroup of | C83×#1469, C2×#329×C83, C83×#1527, … |
| maximal quotient of | C2×#382×C83, C2×#388×C83, C2×#390×C83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 207);