Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C521 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #16861969 |
| commutator, hypocenter | C521 | C32 |
| Fitting | C4×C521 | C8 |
| socle, prime radical | C2×C521 | C16 |
| cosocle | #22552367 | C2 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16672 |
Polycyclic presentation:
2^5,521|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^315,f^b=f^235,f^c=f^520292 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#30659798, #45688539, #45688540, … |
| maximal normal subgroup of | C2×#30659798, #45688539, #45688540, … |
| maximal quotient of | #45688514, C2×#30659798 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 236);