Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#11924078 |
| unambiguous semidirect product | D293⋊(C2×C22⋊C4) |
| unambiguous semidirect product | (C2×#11924078)⋊C23 |
| Fitting | C24×C293 ⋊ C4 |
| Sylow | C293 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
1208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173958, #49173959, #49173966, … |
| maximal normal subgroup of | #49173958, #49173959, #49173966, … |
| maximal quotient of | C22×(C2×#11924078)⋊C4, C2×C4×C22⋊#11924078, C2×#34037070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1610);