Finite Group DatabasebetaFinite Group Databasebeta| order | 238 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C3×C16 (order 96) · Inn(G) = C1 · Out(G) = C2×C3×C16 |
| holomorph | G ⋊ Aut(G) = C2×AGL(1,𝔽7)×AGL(1,𝔽17) |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C238 |
| abelian | C2×C7×C17 |
| multiplicative | (ℤ/239)ˣ, (ℤ/478)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 238 |
A minimal faithful permutation representation — 1 generator on 26 points:
(1,2)(3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(238, 4);