Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#14523438 |
| unambiguous semidirect product | D521⋊(C4⋊C4) |
| Fitting | C2×C4×C521 ⋊ C4 |
| Sylow | C521 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4168 |
1060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45688305, #45688306, #45688311, … |
| maximal normal subgroup of | #45688305, #45688306, #45688311, … |
| maximal quotient of | C2×(C2×#14523438)⋊C4, C4×C4⋊#14523438, #45688374, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 224);