Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C42×C293 ⋊ C4 |
| Sylow | C293 ⋊ #376 |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=e,b^2=f,c^2=d,b^a=bd,g^a=g^138,g^e=g^2921208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173608, #49173672, #49173674, … |
| maximal normal subgroup of | #49173608, #49173672, #49173674, … |
| maximal quotient of | C4×(C2×#11924078)⋊C4, #49173960, #49173961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1485);