Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4×C5 |
| direct product | C22×C4×#1039 |
| derived, Sylow | C52 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | C5⋊D5 |
| commutator, hypocenter | C52 | C22×C42 |
| Frattini | C22 | C23×C5⋊D5 |
| Fitting | C23×C4×C52 | C2 |
| socle, prime radical | C24×C52 | C22 |
| cosocle | C22×C52 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23×C4 | |
1992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C42×C5⋊D5, C22×#11716596, C22×#11716895 |
| maximal normal subgroup of | C22×C42×C5⋊D5, C22×#11716596, C22×#11716895 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9662);