Finite Group DatabasebetaFinite Group Databasebeta| order | 536 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C67⋊C8 |
| derived, Sylow | C67 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D67 |
| commutator, hypocenter | C67 | C8 |
| Fitting, cosocle | C4×C67 | C2 |
| socle, prime radical | C2×C67 | C4 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 536 |
Polycyclic presentation:
2^3,67|a^2=b,b^2=c,d^a=d^66140 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D67, C2×C67⋊C8, #11761611, … |
| maximal normal subgroup of | C8×D67, C2×C67⋊C8, #11761611, … |
| maximal quotient of | C67⋊C16, C2×C67⋊C8, C3×C67⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(536, 1);