Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#11717388 |
| Fitting | C2×C4×C52 ⋊ D4 |
| Sylow | C52 ⋊ C2×#121 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D52⋊C2 |
| commutator, cosocle | C2×C5⋊D5 | C24 |
| Frattini | C2 | C22×D52⋊C2 |
| Fitting | C2×C4×C52 | D4 |
| socle | C22×C52 | C2×D4 |
| hypercenter | C2×C4 | D52⋊C2 |
| hypocenter | C52 | C2×#121 |
| LCS | G ▷ C2×C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
708 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
88 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10022);