Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #578×D89 |
| Fitting | #578×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×#578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D89 |
| commutator, cosocle | C4×C89 | C25 |
| Frattini | C4 | C24×D89 |
| Fitting | #578×C89 | C2 |
| socle | C2×C89 | C23×D4 |
| hypercenter | #578 | D89 |
| hypocenter | C89 | C2×#578 |
| LCS | G ▷ C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #578 | |
1408 conjugacy classes of subgroups.
1012 conjugacy classes — view the full character table.
| maximal subgroup of | #2193×D89, #2195×D89, #36708399, … |
| maximal normal subgroup of | #2193×D89, #2195×D89, #36708399, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 19272);