Finite Group DatabasebetaFinite Group Databasebeta| order | 4072 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C509 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #14523266 |
| commutator, hypocenter | C509 | C8 |
| Fitting, socle, prime radical | C2×C509 | C4 |
| cosocle | Dic509 | C2 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 517 |
| transitive degree | μt(G) = 4072 |
Polycyclic presentation:
2^3,509|a^2=b,b^2=c,d^a=d^301,d^b=d^508262 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4072, 13);