Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×D52 |
| unambiguous semidirect product | (C5×D5)⋊C25 |
| unambiguous semidirect product | (C5⋊D5)⋊C25 |
| Fitting, socle | C24×C52 ⋊ C22 |
| derived, Sylow | C52 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D52 |
| commutator, cosocle, hypocenter | C52 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C24×C52 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C24 | |
12048 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C24×D5⋊AGL(1,𝔽5), C2×#13106387, C2×#13104117, … |
| maximal normal subgroup of | C24×D5⋊AGL(1,𝔽5), C2×#13106387, C2×#13104117, … |
| maximal quotient of | C2×#13107821, #72220977, C22×D4×D52, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10278);