Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×C16×C5⋊D5 |
| Fitting | C2×C52×C16 ⋊ C2 |
| derived, Sylow | C52 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | C5⋊D5 |
| commutator, hypocenter | C52 | C22×C16 |
| Frattini | C8 | C22×C5⋊D5 |
| Fitting | C2×C52×C16 | C2 |
| socle | C22×C52 | C2×C8 |
| prime radical | C22×C5⋊D5 | C8 |
| cosocle | C52×C8 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C16 | |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊D5×#346, C2×C16×#1043, C2×#13100222, … |
| maximal normal subgroup of | C5⋊D5×#346, C2×C16×#1043, C2×#13100222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5114);