Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#22627689 |
| Fitting | C2×Q8×C293 ⋊ C4 |
| Sylow | C293 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 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 |
758 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22627689, #49174549, #49174562, … |
| maximal normal subgroup of | C4×#22627689, #49174549, #49174562, … |
| maximal quotient of | C2×#34036977, C2×Q8⋊#14556880, #49174079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1545);