Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #557×D89 |
| Fitting | #557×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×#557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | #557×C89 | C2 |
| prime radical | C22×D89 | C24 |
| hypercenter | #557 | D89 |
| hypocenter | C89 | C2×#557 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #557 | |
1048 conjugacy classes of subgroups.
1150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1626×D89, #1636×D89, #1648×D89, … |
| maximal normal subgroup of | #1626×D89, #1636×D89, #1648×D89, … |
| maximal quotient of | Q8×C4⋊C4×D89, #2351×D89, #2355×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18078);