Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#22627686 |
| unambiguous semidirect product | D293⋊#102 |
| Fitting | C2×D4×C293 ⋊ C4 |
| Sylow | C293 ⋊ C2×#102 |
202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4688 |
758 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22627686, #102×#11924078, #49174555, … |
| maximal normal subgroup of | C4×#22627686, #102×#11924078, #49174555, … |
| maximal quotient of | C2×D4⋊#14556880, D293⋊(D4⋊C8), C2×#34036977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1537);