Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C52 ⋊ #493 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#6037 |
| commutator, cosocle | C2×C4×C52 | C23 |
| Frattini | C2×C4 | C2×D52 |
| Fitting | C42×C52 | C22 |
| socle | C22×C52 | C2×D4 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #493 |
| LCS | G ▷ C2×C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
368 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^6,5^2|c^2=d,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^4,c^b=cd,e^b=ef,h^b=h^4142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2884);