Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×#6036 |
| derived, Sylow | C52 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D52 |
| commutator, hypocenter | C52 | C24×C4 |
| Frattini | C2 | C23×D52 |
| Fitting, socle | C24×C52 | C22 |
| prime radical | C24×C5⋊D5 | C2 |
| cosocle | C2×C52 | C25 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C24 | |
3472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#87830, #72221631, #72221637, … |
| maximal normal subgroup of | C23×#87830, #72221631, #72221637, … |
| maximal quotient of | #72221063, C23×#87767, C22×C4×#6036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10200);