Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of AGL(1,𝔽5)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#11717300 |
| derived, Sylow | C52 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | AGL(1,𝔽5)2 |
| commutator, hypocenter | C52 | C2×C4×C8 |
| Frattini | C2 | C2×AGL(1,𝔽5)2 |
| Fitting, socle | C22×C52 | C42 |
| prime radical | C22×C5⋊D5 | C2×C4 |
| cosocle | #6036 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22 | |
351 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #72220679, #72221578, C2×#13107464, … |
| maximal normal subgroup of | #72220679, #72221578, C2×#13107464, … |
| maximal quotient of | #72220672, #72221684, D3×#11717300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9814);