Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#14523438 |
| unambiguous semidirect product | D521⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#14523438)⋊C22 |
| Fitting | C23×C521 ⋊ C4 |
| Sylow | C521 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4168 |
1060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45688309, #45688310, C4×C22⋊#14523438, … |
| maximal normal subgroup of | #45688309, #45688310, C4×C22⋊#14523438, … |
| maximal quotient of | C2×(C2×#14523438)⋊C4, C4×C22⋊#14523438, #45688373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 223);