Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#17985381 |
| Fitting | C22×C8×C283 ⋊ C2 |
| Sylow | C283 ⋊ C22×SD16 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
4540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49121594, #49121596, #49121615, … |
| maximal normal subgroup of | #49121594, #49121596, #49121615, … |
| maximal quotient of | C22×#22583532, C22×#22583535, C22×#22583542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1323);