Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #556×D89 |
| Fitting | #556×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×#556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | #556×C89 | C2 |
| prime radical | C2×D4×D89 | C22 |
| hypercenter | #556 | D89 |
| hypocenter | C89 | C2×#556 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #556 | |
1112 conjugacy classes of subgroups.
1150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1628×D89, #1638×D89, #1652×D89, … |
| maximal normal subgroup of | #1628×D89, #1638×D89, #1652×D89, … |
| maximal quotient of | #2347×D89, #2354×D89, #2355×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18052);