Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×#14523438 |
| Fitting | D4×C521 ⋊ C4 |
| Sylow | C521 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2084 |
670 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8×#14523438, SD16×#14523438, #45688471, … |
| maximal normal subgroup of | D8×#14523438, SD16×#14523438, #45688471, … |
| maximal quotient of | C22⋊C4×#14523438, C4⋊C4×#14523438, #45688379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 226);