Finite Group DatabasebetaFinite Group Databasebeta| order | 1160 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C29 · Schur multiplier (H2) = C23 |
| direct product | C22×D5×C29 |
| unambiguous semidirect product | C5⋊(C23×C29) |
| unambiguous semidirect product | (C2×C5)⋊(C22×C29) |
| Fitting, socle | C22×C5×C29 ⋊ C2 |
| derived, Sylow | C5 ⋊ C23×C29 |
| Hall | C5×C29 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C29 | D5 |
| commutator, cosocle, hypocenter | C5 | C23×C29 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C29 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C29 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 580 |
464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D5×C29⋊C7, C22×D5×D29, C22×AGL(1,𝔽5)×C29, … |
| maximal normal subgroup of | C22×D5×C29⋊C7, C22×D5×D29, C22×AGL(1,𝔽5)×C29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1160, 47);