Finite Group DatabasebetaFinite Group Databasebeta| order | 1160 |
| isoclinism | isoclinic class of #10596814 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#10596814 |
| Fitting, socle | C2×C5×C29 ⋊ C4 |
| derived, Hall | C5×C29 ⋊ C2×C4 |
| Sylow | C29 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10596814 |
| commutator, hypocenter | C5×C29 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C29 | C4 |
| prime radical | C2×D145 | C2 |
| cosocle | D145 | C22 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 290 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10596814⋊C7, C2×D5⋊#1181, C22×#10596814 |
| maximal normal subgroup of | C2×#10596814⋊C7, C2×D5⋊#1181, C22×#10596814 |
| maximal quotient of | C22×#10596814 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1160, 42);