Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | Aut(G) = C22×AGL(1,𝔽5)×#120 (order 2560) · Inn(G) = C2×D5 · Out(G) = C22×C4×D4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D20 |
| Fitting | C42×C5 ⋊ C2 |
| Sylow | C5 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D5 |
| commutator | C2×C5 | C22×C4 |
| Frattini | C22 | C22×D5 |
| Fitting | C42×C5 | C2 |
| socle, cosocle | C22×C5 | C23 |
| prime radical | C2×D20 | C2 |
| hypercenter | C42 | D5 |
| hypocenter | C5 | C4×D4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2,4,5,3)(10,11,12,13);(2,3)(4,5)(11,13);(6,7,8,9)52 conjugacy classes — view the full character table.
| maximal subgroup of | #64679, #64703, C8×D20, … |
| maximal normal subgroup of | #64679, #64703, C8×D20, … |
| maximal quotient of | #64942, #64954, #64957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 94);