Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C52×Q8 ⋊ C22 |
| Sylow | C52 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D52 |
| commutator, socle, cosocle | C2×C52 | C25 |
| Fitting | C2×C52×Q8 | C22 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #585 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
1766 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|c^2=f,e^2=f,e^a=ef,g^a=g^4,d^b=df,h^b=h^4,e^c=ef148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10186);