Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#87879 |
| Sylow | C52 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D52 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C23×D52 |
| Fitting | C24×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | C22×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C24 | |
2016 conjugacy classes of subgroups; only the 568 normal subgroups are shown.
This group has 2016 conjugacy classes of subgroups — too many to draw. Only its 568 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11717477, C2×#13106188 |
| maximal normal subgroup of | C22×#11717477, C2×#13106188 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10198);