Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#14523438 |
| unambiguous semidirect product | D521⋊C42 |
| Fitting | C2×C4×C521 ⋊ C4 |
| derived, Sylow | C521 ⋊ C2×C42 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4168 |
1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45688297, #45688302, #45688304, … |
| maximal normal subgroup of | #45688297, #45688302, #45688304, … |
| maximal quotient of | C42×#14523438, C2×(C2×#14523438)⋊C4, #45688368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 222);