Finite Group DatabasebetaFinite Group Databasebeta| order | 1160 |
| isoclinism | isoclinic class of D5×D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×D29 |
| unambiguous semidirect product | (D5×C29)⋊C22 |
| unambiguous semidirect product | (C5×D29)⋊C22 |
| unambiguous semidirect product | D145⋊C22 |
| Fitting, socle | C2×C5×C29 ⋊ C22 |
| derived, Hall | C5×C29 ⋊ C23 |
| Sylow | C29 ⋊ C22×D5 |
| Sylow | C5 ⋊ C22×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×D29 |
| commutator, cosocle, hypocenter | C5×C29 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C29 | C22 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 290 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×D29⋊C7, C2×D5×#1181, C2×AGL(1,𝔽5)×D29, … |
| maximal normal subgroup of | C2×D5×D29⋊C7, C2×D5×#1181, C2×AGL(1,𝔽5)×D29, … |
| maximal quotient of | C22×D5×D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1160, 45);