Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C571 ⋊ C2 |
| Sylow | C571 ⋊ #102 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
Polycyclic presentation:
2^5,571|a^2=d,c^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^5702864 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D571, C2×#32912614, #49142260, … |
| maximal normal subgroup of | #102×D571, C2×#32912614, #49142260, … |
| maximal quotient of | #49141993, #49141999, #49142009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 66);