Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C293 ⋊ #362 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=f,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^292,c^b=cef,d^b=df,e^b=ef,g^b=g^2922936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #362×D293, C2×#34035946, #49160531, … |
| maximal normal subgroup of | #362×D293, C2×#34035946, #49160531, … |
| maximal quotient of | #49156756, #49156804, #49156835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 366);