Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C52 ⋊ #533 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Frattini | C22 | C22×D52 |
| Fitting | C42×C52 | C22 |
| prime radical | C22×C5×D5 | C23 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #533 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
514 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^6,5^2|a^2=f,c^2=e,d^2=f,d^a=df,g^a=g^4,d^b=de,h^b=h^4172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7342);