Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C24 |
| direct product | #539×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C83 |
| prime radical | #121×C83 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ G | |
218 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1826 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#1597, C83×#1603, C83×#1609, … |
| maximal normal subgroup of | C83×#1597, C83×#1603, C83×#1609, … |
| maximal quotient of | C83×#2313, C83×#2318, C83×#2322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 220);