Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C22⋊#11924078 |
| Fitting | C22×C4×C293 ⋊ C4 |
| Sylow | C293 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4688 |
1208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173626, #49173627, #49173632, … |
| maximal normal subgroup of | #49173626, #49173627, #49173632, … |
| maximal quotient of | C4×(C2×#11924078)⋊C4, #49173959, #49173961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1486);