Finite Group DatabasebetaFinite Group Databasebeta| order | 36224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#121×C283 ⋊ C2 |
| Sylow | C283 ⋊ #3534 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D283 |
| commutator, socle, cosocle | C22×C283 | C25 |
| Fitting | C2×#121×C283 | C2 |
| hypercenter | C2×#121 | D283 |
| hypocenter | C283 | #3534 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ C2×#121 | |
1166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^7,283|d^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^282,c^b=cg,d^b=df3986 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36224, 18700);