Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#22627536 |
| Fitting | C22×C8×C293 ⋊ C2 |
| Sylow | C293 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9376 |
4712 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49156708, #49158542, C4×#22627536, … |
| maximal normal subgroup of | #49156708, #49158542, C4×#22627536, … |
| maximal quotient of | C2×#34035852, C2×#34035854, #49157097, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 509);