Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C22×C52 ⋊ Dic3 |
| Hall | C52⋊C3 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ #217 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^a=bd,e^a=e^2,f^a=f^3g^3,g^a=g^2,f^c=f^4,g^c=g^4,f^e=fg,g^e=f^2g^326 conjugacy classes — view the full character table.
| maximal subgroup of | #72227925 |
| maximal quotient of | #72227925 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 498);