Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C293 ⋊ #368 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=ce,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^138,g^b=g^292,g^d=g^2921190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173940, #49173941, #49173950, … |
| maximal normal subgroup of | #49173940, #49173941, #49173950, … |
| maximal quotient of | #49173817, #49173818, #49173845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1478);