Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C293 ⋊ C2 |
| Sylow | C293 ⋊ #519 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,g^d=g^2922954 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49167621, #49167623, #49167625, … |
| maximal normal subgroup of | #49167621, #49167623, #49167625, … |
| maximal quotient of | #49161139, #49161149, #49161150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1025);