Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C521 ⋊ M32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8336 |
Polycyclic presentation:
2^5,521|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^315,f^b=f^520,f^c=f^235,f^d=f^520280 conjugacy classes — view the full character table.
| maximal subgroup of | #45688532, #45688533, #45688536, … |
| maximal normal subgroup of | #45688532, #45688533, #45688536, … |
| maximal quotient of | #45688526, #45688529, C4⋊#22552376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 243);