Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C293 ⋊ C4 |
| Sylow | C293 ⋊ #354 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^138,c^b=cf,d^b=def,d^c=df,g^d=g^292743 conjugacy classes — view the full character table.
| maximal subgroup of | #49173908, #49173909, C2×#34037035, … |
| maximal normal subgroup of | #49173908, #49173909, C2×#34037035, … |
| maximal quotient of | #49173715, #49173726, #49173765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1455);