Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11716940 |
| Sylow | C52 ⋊ C2×#135 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #6037 |
| commutator, cosocle | C4×C52 | C24 |
| Frattini | C4 | C22×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C22×C52 | C2×D4 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | C2×#135 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
608 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8265);