Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6053 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#11716729 |
| derived, Sylow | C52 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #6053 |
| commutator, hypocenter | C52 | C2×C32 |
| Frattini | C4 | C2×#6053 |
| Fitting | C2×C4×C52 | C8 |
| socle, prime radical | C22×C52 | C16 |
| cosocle | #87764 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
88 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5756);