Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D571)⋊C4 |
| Fitting | C22⋊C4×C571 ⋊ C2 |
| Sylow | C571 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
Polycyclic presentation:
2^5,571|a^2=e,c^2=e,b^a=bd,f^c=f^5702870 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D4×D571, C2×(C22⋊D571)⋊C4, C4×#22603732, … |
| maximal normal subgroup of | C4×D4×D571, C2×(C22⋊D571)⋊C4, C4×#22603732, … |
| maximal quotient of | #49142113, C22⋊C4×Dic571, #49142117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 106);