Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C293 ⋊ #433 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^138,c^b=cf,g^b=g^292,g^e=g^292758 conjugacy classes — view the full character table.
| maximal subgroup of | D293⋊#433, C2×#34037154, #49175466, … |
| maximal normal subgroup of | D293⋊#433, C2×#34037154, #49175466, … |
| maximal quotient of | #49174504, #49174514, #49174573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1574);