Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M64×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D89 |
| commutator, socle | C2×C89 | C22×C16 |
| Fitting | M64×C89 | C2 |
| prime radical | #13083574 | C8 |
| cosocle | C16×C89 | C23 |
| hypercenter | M64 | D89 |
| hypocenter | C89 | #2258 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C16 ◁ M64 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^88,c^b=cg,h^c=h^881840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36474989, #36474991, #36474994, … |
| maximal normal subgroup of | #36474989, #36474991, #36474994, … |
| maximal quotient of | #36474609, #36474610, #36474623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6805);