Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊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^b=f^570,f^c=f^5702870 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49142346, #49142348, #49142351, … |
| maximal normal subgroup of | #49142346, #49142348, #49142351, … |
| maximal quotient of | #49142113, C4⋊C4×Dic571, #49142137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 108);