Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| isoclinism | isoclinic class of D89 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×C32×D89 |
| Fitting | C2×C32×C89 ⋊ C2 |
| derived, Sylow | C89 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D89 |
| commutator, hypocenter | C89 | C22×C32 |
| Frattini | C16 | C22×D89 |
| Fitting | C2×C32×C89 | C2 |
| socle | C22×C89 | C2×C16 |
| prime radical | C22×D89 | C16 |
| cosocle | C16×C89 | C23 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
2944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36442236, C4×C32×D89, #1397×D89, … |
| maximal normal subgroup of | #36442236, C4×C32×D89, #1397×D89, … |
| maximal quotient of | C4×C32×D89, C2×C32×Dic89, C22⋊C32×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6798);