Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Sylow | C5×C25 ⋊ Q8 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1000 |
Polycyclic presentation:
2^3,5^3|a^2=c,b^2=c,d^5=f,b^a=bc,d^a=d^4f^4,e^a=e^4,f^a=f^4253 conjugacy classes — view the full character table.
| maximal subgroup of | #14522114, #14522117, #14522123, … |
| maximal normal subgroup of | #14522114, #14522117, #14522123, … |
| maximal quotient of | #14522228, C4⋊#92524, C2×#11758682 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 67);