Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊C4×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C83 | C22 |
| commutator | C2 | C23×C4×C83 |
| Frattini, cosocle | C22 | C24×C83 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C83 ◁ G | |
418 conjugacy classes of subgroups.
3320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×C4⋊#95, C83×#1436, C83×#1439, … |
| maximal normal subgroup of | C83×C4⋊#95, C83×#1436, C83×#1439, … |
| maximal quotient of | C22×#95×C83, C2×C4×C4⋊C4×C83, C2×#380×C83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 194);