Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | #125×D173 |
| Fitting | #125×C173 ⋊ C2 |
| Sylow | C173 ⋊ C2×#125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D173 |
| commutator, socle, cosocle | C22×C173 | C24 |
| Fitting | #125×C173 | C2 |
| prime radical | C22×D173 | C23 |
| hypercenter | #125 | D173 |
| hypocenter | C173 | C2×#125 |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ #125 | |
226 conjugacy classes of subgroups.
1232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #330×D173, #36352163, #36352188, … |
| maximal normal subgroup of | #330×D173, #36352163, #36352188, … |
| maximal quotient of | #382×D173, #387×D173, #389×D173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 1068);