Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q8×C293 ⋊ C4 |
| Sylow | C293 ⋊ #421 |
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^138,c^b=cf,d^b=df,g^b=g^292,g^c=g^292,g^e=g^292752 conjugacy classes — view the full character table.
| maximal subgroup of | #49174636, #49174637, #49174782, … |
| maximal normal subgroup of | #49174636, #49174637, #49174782, … |
| maximal quotient of | #49174083, #49174086, #49174087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1548);