Finite Group DatabasebetaFinite Group Databasebeta| order | 1160 |
| isoclinism | isoclinic class of #10596816 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C5×C29 ⋊ C8 |
| Sylow | C29 ⋊ #170 |
| Sylow | C5 ⋊ #6597 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #10596816 |
| commutator, hypocenter | C5×C29 | C8 |
| Fitting, socle, prime radical | C2×C5×C29 | C4 |
| cosocle | Dic5×C29 | C2 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 1160 |
Polycyclic presentation:
2^3,5,29|a^2=b,b^2=c,d^a=d^2,e^a=e^28,d^b=d^4122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1160, 9);