Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#22627581 |
| Fitting | C2×C42×C293 ⋊ C2 |
| Sylow | C293 ⋊ C2×#117 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
4712 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49157097, #49157117, #49158480, … |
| maximal normal subgroup of | #49157097, #49157117, #49158480, … |
| maximal quotient of | C2×#34035975, C2×C4×#17989779, C2×C4×#17989781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1003);