Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C52 ⋊ #578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D52 |
| commutator, cosocle | C4×C52 | C24 |
| Frattini | C4 | C22×D52 |
| Fitting | C52×SD16 | C22 |
| socle | C2×C52 | C22×D4 |
| hypercenter | SD16 | D52 |
| hypocenter | C52 | #578 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
558 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|c^2=f,e^2=f,b^a=bf,d^a=df,g^a=g^4,d^b=df,h^b=h^4,d^c=de,e^c=ef,e^d=ef94 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8195);