Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C23×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ #518 |
703 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=e,d^a=df,g^a=g^2,c^b=cf,h^b=h^4,g^e=g^4100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#66258, #72221747, #72221748, … |
| maximal normal subgroup of | D5×#66258, #72221747, #72221748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10005);