Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C42×D521 |
| Fitting | C42×C521 ⋊ C2 |
| derived, Sylow | C521 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D521 |
| commutator, hypocenter | C521 | C2×C42 |
| Frattini | C22 | C22×D521 |
| Fitting | C42×C521 | C2 |
| socle, cosocle | C22×C521 | C23 |
| prime radical | C22×D521 | C22 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C42 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8336 |
4192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C8×D521, #97×D521, C4×#22552347, … |
| maximal normal subgroup of | C4×C8×D521, #97×D521, C4×#22552347, … |
| maximal quotient of | C42×Dic521, #95×D521, #45687277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 94);