Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #2775 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | #393×C89 | C2 |
| prime radical | C24×C89 | C23 |
| hypercenter | #393 | D89 |
| hypocenter | C89 | #2775 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #393 | |
386 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=fg,b^2=f,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^88,c^b=cg,d^b=de,h^b=h^88,h^d=h^881000 conjugacy classes — view the full character table.
| maximal subgroup of | #36763346, #36763355, #36763386, … |
| maximal normal subgroup of | #36763346, #36763355, #36763386, … |
| maximal quotient of | #36482147, #36482276, #36482327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 12088);