Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C24 |
| direct product | #553×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C83 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ G | |
238 conjugacy classes of subgroups.
2075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#3297, C83×#3301, C83×#3307, … |
| maximal normal subgroup of | C83×#3297, C83×#3301, C83×#3307, … |
| maximal quotient of | C83×#2345, C83×#2347, C83×#2352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 234);