Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#11924078)⋊C8 |
| Fitting | C2×C8×C293 ⋊ C4 |
| Sylow | C293 ⋊ #336 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=e,d^2=f,b^a=bc,g^b=g^138,g^e=g^2921208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×(C2×#11924078)⋊C8, #49174447, #49174450, … |
| maximal normal subgroup of | C2×(C2×#11924078)⋊C8, #49174447, #49174450, … |
| maximal quotient of | #49173607, #49173608, #49173610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1414);