Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D571)⋊C4 |
| Fitting | C22×C4×C571 ⋊ C2 |
| Sylow | C571 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
4580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49141989, #49142113, C4×(C2×D571)⋊C4, … |
| maximal normal subgroup of | #49141989, #49142113, C4×(C2×D571)⋊C4, … |
| maximal quotient of | C2×C571⋊#95, C4×(C2×D571)⋊C4, #49142121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 97);