Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C293 ⋊ C2 |
| Sylow | C293 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^292,c^b=ce,g^b=g^2924700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D293, C2×#34035858, #49157166, … |
| maximal normal subgroup of | D4⋊C8×D293, C2×#34035858, #49157166, … |
| maximal quotient of | #49156605, #49156607, #49156625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 278);