Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C17×M128 ⋊ C2 |
| Sylow | C17 ⋊ #13737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C22×D17 |
| commutator, socle | C2×C17 | C22×C32 |
| Fitting | C17×M128 | C2 |
| prime radical | #63252 | C16 |
| cosocle | C17×C32 | C23 |
| hypercenter | M128 | D17 |
| hypocenter | C17 | #13737 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C32 ◁ M128 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^8,17|a^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^16,c^b=ch,i^c=i^16800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 90608);