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 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#16861969 |
| commutator, socle | C2×C521 | C2×C8 |
| Fitting, prime radical | C22×C521 | C8 |
| cosocle | #16861967 | C22 |
| hypercenter | C22 | #16861969 |
| hypocenter | C521 | M32 |
| LCS | G ▷ C2×C521 ▷ C521 | |
| UCS | C1 ◁ C2 ◁ C22 | |
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^c=f^235,f^d=f^520280 conjugacy classes — view the full character table.
| maximal subgroup of | #45688530, #45688531, C2×#30659804, … |
| maximal normal subgroup of | #45688530, #45688531, C2×#30659804, … |
| maximal quotient of | #45688526, C22⋊#22552376, #45688535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 242);