Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C4×C547 ⋊ C2 |
| Sylow | C547 ⋊ #123 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8752 |
Polycyclic presentation:
2^5,547|c^2=d,b^a=bd,c^a=ce,f^a=f^5464382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46855190, #123×D547, C2×#31775985, … |
| maximal normal subgroup of | #46855190, #123×D547, C2×#31775985, … |
| maximal quotient of | #46854864, #46854874, #46854880, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 129);