Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | D4×Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3514 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | D4×Q8×C89 | C2 |
| hypercenter | D4×Q8 | D89 |
| hypocenter | C89 | #3514 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1142 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|c^2=f,e^2=g,b^a=bf,c^a=cg,e^a=ef,h^a=h^88,d^b=df,h^c=h^88,h^e=h^881144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36531225, #36531233, #36531240, … |
| maximal normal subgroup of | #36531225, #36531233, #36531240, … |
| maximal quotient of | #36714604, #36715086, #36715131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18472);