Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C83 · Schur multiplier (H2) = C22 |
| direct product | C2×SD32×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | D8 |
| commutator, Frattini, cosocle | C8 | C23×C83 |
| prime radical | C2×D8×C83 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C4×C83 ◁ C2×C8×C83 ◁ G | |
90 conjugacy classes of subgroups.
1826 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×SD32×C83, C83×#2175, C83×#2185, … |
| maximal normal subgroup of | C4×SD32×C83, C83×#2175, C83×#2185, … |
| maximal quotient of | C2×#357×C83, C2×#358×C83, C2×#367×C83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 187);