Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #578×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3584 |
| 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 | #3584 |
| LCS | G ▷ C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #578 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,d^c=dg,h^c=h^88,h^d=h^88,h^e=h^881012 conjugacy classes — view the full character table.
| maximal subgroup of | #36708381, #36708387, #36708410, … |
| maximal normal subgroup of | #36708381, #36708387, #36708410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 19280);