Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C571⋊C16 |
| unambiguous semidirect product | (C2×C571)⋊C16 |
| derived, Sylow | C571 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D571 |
| commutator, hypocenter | C571 | C2×C16 |
| Frattini | C8 | C2×D571 |
| Fitting | C2×C8×C571 | C2 |
| socle, prime radical | C22×C571 | C8 |
| cosocle | C8×C571 | C22 |
| LCS | G ▷ C571 | |
| UCS | C1 ◁ C2×C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18272 |
4592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic571, C4×C571⋊C16, #49142041, … |
| maximal normal subgroup of | C16×Dic571, C4×C571⋊C16, #49142041, … |
| maximal quotient of | C4×C571⋊C16, C22⋊(C571⋊C16), C4⋊(C571⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 84);