Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#22627683 |
| Fitting | C22×C4×C293 ⋊ C4 |
| Sylow | C293 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4688 |
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173879, #49173880, #49174530, … |
| maximal normal subgroup of | #49173879, #49173880, #49174530, … |
| maximal quotient of | C2×#34036973, C2×#34036974, #49174022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1527);