Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C283 ⋊ C2 |
| Sylow | C283 ⋊ #431 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^2824552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#17985375, #49119540, #49119543, … |
| maximal normal subgroup of | C8×#17985375, #49119540, #49119543, … |
| maximal quotient of | #49121006, C4×(C2×D283)⋊C8, C4×Dic283⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 600);