Finite Group DatabasebetaFinite Group Databasebeta| order | 5728 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C179 · Schur multiplier (H2) = C2 |
| direct product | #126×C179 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C179 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C179 |
| prime radical | C23×C179 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C179 ◁ G | |
60 conjugacy classes of subgroups.
2506 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#126×C179, #529×C179, #538×C179, … |
| maximal normal subgroup of | C2×#126×C179, #529×C179, #538×C179, … |
| maximal quotient of | #383×C179, #387×C179, #388×C179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5728, 33);