Finite Group DatabasebetaFinite Group Databasebeta| order | 4288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #95×C67 ⋊ C2 |
| Sylow | C67 ⋊ #399 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D67 |
| commutator, socle, cosocle | C23×C67 | C23 |
| Fitting | #95×C67 | C2 |
| prime radical | C23×D67 | C22 |
| hypercenter | #95 | D67 |
| hypocenter | C67 | #399 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #95 | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2144 |
Polycyclic presentation:
2^6,67|a^2=d,b^2=de,b^a=bd,c^a=ce,c^b=cf,g^b=g^66,g^c=g^66682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4288, 486);