Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | #126×D293 |
| Fitting | #126×C293 ⋊ C2 |
| Sylow | C293 ⋊ C2×#126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | #126×C293 | C2 |
| prime radical | C23×D293 | C22 |
| hypercenter | #126 | D293 |
| hypocenter | C293 | C2×#126 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ #126 | |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
2072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#126×D293, #529×D293, #538×D293, … |
| maximal normal subgroup of | C2×#126×D293, #529×D293, #538×D293, … |
| maximal quotient of | #383×D293, #387×D293, #388×D293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1072);