Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#17989781 |
| Sylow | C293 ⋊ C4×C4⋊C4 |
194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18752 |
4712 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49158646, C8×#17989781, #49158651, … |
| maximal normal subgroup of | #49158646, C8×#17989781, #49158651, … |
| maximal quotient of | C4×#22627531, #49157011, #49157013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 402);