Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C89 ⋊ #2767 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator, socle, prime radical, cosocle | C23×C89 | C24 |
| Fitting | #387×C89 | C2 |
| hypercenter | #387 | D89 |
| hypocenter | C89 | #2767 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #387 | |
344 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=g,b^2=ef,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^88,h^d=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36762397, #36762408, #36762690, … |
| maximal normal subgroup of | #36762397, #36762408, #36762690, … |
| maximal quotient of | #36482124, #36482251, #36482337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 11972);