Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C283 ⋊ #419 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|a^2=e,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^282,c^b=cf,d^b=df2842 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49121233, #49121236, #49121632, … |
| maximal normal subgroup of | #49121233, #49121236, #49121632, … |
| maximal quotient of | #49119656, #49119682, #49119708, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 558);