Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | #126×D173 |
| Fitting | #126×C173 ⋊ C2 |
| Sylow | C173 ⋊ C2×#126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D173 |
| commutator, socle, cosocle | C22×C173 | C24 |
| Fitting | #126×C173 | C2 |
| prime radical | C23×D173 | C22 |
| hypercenter | #126 | D173 |
| hypocenter | C173 | C2×#126 |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ #126 | |
246 conjugacy classes of subgroups.
1232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#126×D173, #529×D173, #538×D173, … |
| maximal normal subgroup of | C2×#126×D173, #529×D173, #538×D173, … |
| maximal quotient of | #383×D173, #387×D173, #388×D173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 1072);