Finite Group DatabasebetaFinite Group Databasebeta| order | 36224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #556×C283 ⋊ C2 |
| Sylow | C283 ⋊ #3523 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D283 |
| commutator, socle, cosocle | C22×C283 | C25 |
| Fitting | #556×C283 | C2 |
| prime radical | #22583581 | C22 |
| hypercenter | #556 | D283 |
| hypocenter | C283 | #3523 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #556 | |
992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18112 |
Polycyclic presentation:
2^7,283|a^2=f,b^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^282,h^c=h^282,h^e=h^2823569 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36224, 18605);