Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #87863 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4×C5 |
| direct product | C4×C4⋊#1044 |
| Fitting | C42×C52 ⋊ C4 |
| Sylow | C52 ⋊ C4×C4⋊C4 |
496 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #72220765, #72220783, C4×#11717363, … |
| maximal normal subgroup of | #72220765, #72220783, C4×#11717363, … |
| maximal quotient of | #72220724, #72220906, C2×C4×C4⋊#1044 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7177);