Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×Dic523 |
| derived, Sylow | C523 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D523 |
| commutator, hypocenter | C523 | C4×C8 |
| Frattini | C2×C4 | C2×D523 |
| Fitting | C2×C8×C523 | C2 |
| socle, prime radical | C22×C523 | C2×C4 |
| cosocle | C2×C4×C523 | C22 |
| LCS | G ▷ C523 | |
| UCS | C1 ◁ C2×C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16736 |
4208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic523, #45689980, Dic523⋊C16, … |
| maximal normal subgroup of | C16×Dic523, #45689980, Dic523⋊C16, … |
| maximal quotient of | C8×C523⋊C8, #45689927, #45689959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 54);