Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C521 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D521 |
| commutator, socle, prime radical, cosocle | C22×C521 | C23 |
| Fitting | C4⋊C4×C521 | C2 |
| hypercenter | C4⋊C4 | D521 |
| hypocenter | C521 | C4⋊Q8 |
| LCS | G ▷ C22×C521 ▷ C521 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16672 |
Polycyclic presentation:
2^5,521|a^2=d,b^2=d,c^2=e,b^a=bd,c^a=ce,f^b=f^5202614 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45687710, #45687711, #45687715, … |
| maximal normal subgroup of | #45687710, #45687711, #45687715, … |
| maximal quotient of | #45687301, #45687328, #45687329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 145);