Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×#11716583 |
| derived, Sylow | C52 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D52 |
| commutator, hypocenter | C52 | C22×C16 |
| Frattini | C8 | C2×D52 |
| Fitting | C2×C52×C8 | C22 |
| socle | C22×C52 | C2×C8 |
| prime radical | C22×C5⋊D5 | C8 |
| cosocle | C52×C8 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C8 | |
272 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 272 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) = 160 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #72242157, C2×#13099848, C2×#13099850, … |
| maximal normal subgroup of | #72242157, C2×#13099848, C2×#13099850, … |
| maximal quotient of | #72269143 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3156);