Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C52 ⋊ C2×#102 |
640 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=e,b^2=e,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=cd,d^b=df,h^b=h^4,d^c=df124 conjugacy classes — view the full character table.
| maximal subgroup of | #72220757, #72220792, #72220800, … |
| maximal normal subgroup of | #72220757, #72220792, #72220800, … |
| maximal quotient of | #72220707, #72223188 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3939);