Finite Group DatabasebetaFinite Group Databasebeta| order | 1160 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D145 |
| Fitting | C22×C5×C29 ⋊ C2 |
| Hall | C5×C29 ⋊ D4 |
| Sylow | C29 ⋊ C22⋊D5 |
| Sylow | C5 ⋊ C22⋊D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D145 |
| commutator, socle, cosocle | C2×C5×C29 | C22 |
| Fitting | C22×C5×C29 | C2 |
| hypercenter | C22 | D145 |
| hypocenter | C5×C29 | D4 |
| LCS | G ▷ C2×C5×C29 ▷ C5×C29 | |
| UCS | C1 ◁ C2 ◁ C22 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 580 |
Polycyclic presentation:
2^3,5,29|b^a=bc,d^a=d^4,e^a=e^28293 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1160, 32);