Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | #568×D89 |
| Fitting | #568×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D89 |
| commutator, socle | C2×C89 | C24×C4 |
| Fitting | #568×C89 | C2 |
| prime radical | C2×#41×D89 | C2 |
| cosocle | C4×C89 | C25 |
| hypercenter | #568 | D89 |
| hypocenter | C89 | C2×#568 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1460 conjugacy classes of subgroups.
1564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1858×D89, #36555272, #1861×D89, … |
| maximal normal subgroup of | #1858×D89, #36555272, #1861×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 19217);