Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#22552376 |
| derived, Sylow | C521 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #16861969 |
| commutator, hypocenter | C521 | C2×C16 |
| Frattini | C2 | C2×#16861969 |
| Fitting, socle, prime radical | C22×C521 | C8 |
| cosocle | #16861967 | C22 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C22 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16672 |
292 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22552376, #45688526, C22⋊#22552376, … |
| maximal normal subgroup of | C4×#22552376, #45688526, C22⋊#22552376, … |
| maximal quotient of | C4×#22552376, C22⋊#22552376, C4⋊#22552376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 240);