Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C52 ⋊ #347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | Dic52 |
| commutator | C4×C52 | C42 |
| Frattini, hypercenter | C2×C8 | D52 |
| Fitting, cosocle | C2×C52×C8 | C22 |
| socle | C2×C52 | #97 |
| prime radical | C22×C52 | M16 |
| hypocenter | C52 | #347 |
| LCS | G ▷ C4×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C2×C8 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=c,c^2=e,d^2=e,e^2=f,b^a=be,c^a=cf,h^a=h^4,d^b=df,g^b=g^4166 conjugacy classes — view the full character table.
| maximal subgroup of | #72220685, #72220752, #72220754, … |
| maximal normal subgroup of | #72220685, #72220752, #72220754, … |
| maximal quotient of | #72242171 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1628);