Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C42×Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #36592 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D89 |
| commutator, socle, cosocle | C23×C89 | C25 |
| Fitting | C42×Q8×C89 | C2 |
| hypercenter | C42×Q8 | D89 |
| hypocenter | C89 | #36592 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C42×Q8 | |
4122 conjugacy classes of subgroups; only the 883 normal subgroups are shown.
This group has 4122 conjugacy classes of subgroups — too many to draw. Only its 883 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=h,b^2=fh,c^2=gh,d^2=h,e^2=h,b^a=bf,c^a=cg,i^a=i^88,c^b=ch,e^b=eh,d^c=dh,e^d=eh3590 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 375156);